AustinRochford/basc_ccs.ipynb

## basc_ccs.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e5803197",
   "metadata": {},
   "source": [
    "---\n",
    "title: A Bayesian Alternative to Synthetic Control Comparative Case Studies in Python with PyMC3\n",
    "tags: PyMC3, Causal Inference, Bayesian Statistics, Python\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed80ec34",
   "metadata": {},
   "source": [
    "Recently I had cause to be perusing [Yiqing Xu's research](https://yiqingxu.org/research/) and dove deep into the 2020 paper _A Bayesian Alternative to Synthetic Control for Comparative Case Studies_^[Pang, Xun, Licheng Liu, and Yiqing Xu. \"A Bayesian alternative to synthetic control for comparative case studies.\" [_Available at SSRN_](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3649226#) (2020).] (BASC-CCS from now on).  In an effort to better understand the method introduced in this paper, I decided to replicate (most of) the results form the simulation study described in Sections 4.1 and A.4.1 in Python using PyMC3.\n",
    "\n",
    "BASC-CCS uses [time series cross sectional data](https://en.wikipedia.org/wiki/Cross-sectional_data) (TSCS) to infer causal effects from observational data where direct control of the treatment mechanism is not possible.  As such it falls under the umbrella of [causal inference methods](https://en.wikipedia.org/wiki/Causal_inference). More specifically, it uses the Bayesian approach that treats causal inference from observational data as a problem of imputing missing (control) data for treated units.\n",
    "\n",
    "**TODO: relationship to other causal inference methods with TSCS data**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80c27426",
   "metadata": {},
   "source": [
    "## Generate the Data\n",
    "\n",
    "We begin by generating the data to be modeled. First we make the necessary Python imports and do some light housekeeping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "95f5a080",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8cbef0c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from warnings import filterwarnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "9c6b12df",
   "metadata": {},
   "outputs": [],
   "source": [
    "from aesara import tensor as at\n",
    "import arviz as az\n",
    "import matplotlib as mpl\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.lines import Line2D\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "import xarray as xr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "36d45c52",
   "metadata": {},
   "outputs": [],
   "source": [
    "filterwarnings('ignore', category=pm.ImputationWarning, module='pymc3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4fcd2742",
   "metadata": {},
   "outputs": [],
   "source": [
    "mpl.rcParams['figure.figsize'] = (8, 6)\n",
    "\n",
    "sns.set(color_codes=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c7db89a",
   "metadata": {},
   "source": [
    "BASC-CCS is designed for TSCS where a number of units are observed over a period of time.  Following the BASC-CCS paper, we simulate data from $N = 50$ units over $T = 30$ time periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "22a319c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 50\n",
    "T = 30\n",
    "\n",
    "t = np.arange(T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e0ec3cd",
   "metadata": {},
   "source": [
    "In this simulation 10% of the units will be treated starting at time $T_{\\mathrm{treat}} = 21$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "82c05b86",
   "metadata": {},
   "outputs": [],
   "source": [
    "T_treat = 21\n",
    "P_treat = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5c56eef",
   "metadata": {},
   "source": [
    "Which units are treated will be determined by a linear combination of two unobserved latent factors, drawn from a standard normal distribution for each unit, $\\Gamma_{i, 1}, \\Gamma_{i, 2} \\sim N(0, 1)$ (note that we use capital letters for simulated quantities and the corresponding lowercase letters for the corresponding inferred parameters)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f74526e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "SEED = 12345 # for reproducibility\n",
    "\n",
    "rng = np.random.default_rng(SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "977b46ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "Γ = rng.normal(size=(N, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "067a9156",
   "metadata": {},
   "source": [
    "Treatment is determined according to the variable\n",
    "\n",
    "$$\\mathrm{tr}_i = 0.7 \\cdot \\Gamma_{i, 1} + 0.3 \\cdot \\Gamma_{i, 2} + \\varepsilon^{\\Gamma}_i,$$\n",
    "\n",
    "where $\\varepsilon^{\\Gamma}_i \\sim N(0, 2^{-2}).$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7e6c4397",
   "metadata": {},
   "outputs": [],
   "source": [
    "tr = Γ.dot([0.7, 0.3]) + rng.normal(0., 0.25, size=N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5a510b0",
   "metadata": {},
   "source": [
    "The five units with the largest values of $tr_i$ are treated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a1ed8ee5",
   "metadata": {},
   "outputs": [],
   "source": [
    "treat_crit = np.percentile(tr, 100 * (1. - P_treat))\n",
    "treated = tr > treat_crit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "2fdc4c88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_treated = treated.sum()\n",
    "\n",
    "n_treated"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "822da1a6",
   "metadata": {},
   "source": [
    "The following plot shows the relationship between the latent values $\\Gamma_i$ and which units are treated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f05b99ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "CMAP = 'winter'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7e2095a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "ax.set_aspect('equal');\n",
    "\n",
    "\n",
    "norm = plt.Normalize(tr.min(), tr.max())\n",
    "sns.scatterplot(x=Γ[~treated, 0], y=Γ[~treated, 1], hue=tr[~treated],\n",
    "                hue_norm=norm, palette=CMAP,\n",
    "                label=\"Untreated\", legend=False,\n",
    "                ax=ax);\n",
    "sns.scatterplot(x=Γ[treated, 0], y=Γ[treated, 1], hue=tr[treated],\n",
    "                s=100, marker='s',\n",
    "                hue_norm=norm, palette=CMAP,\n",
    "                label=\"Treated\", legend=False,\n",
    "                ax=ax);\n",
    "\n",
    "Γ_mult = 1.05\n",
    "Γ_min, Γ_max = Γ_mult * Γ.min(), Γ_mult * Γ.max()\n",
    "plot_Γ = np.linspace(Γ_min, Γ_max, 100)\n",
    "\n",
    "ax.plot(plot_Γ, (treat_crit - 0.7 * plot_Γ) / 0.3,\n",
    "        c='k', ls='--', label=\"Treatment threshold\\n(noiseless)\");\n",
    "\n",
    "sm = plt.cm.ScalarMappable(norm=norm, cmap=CMAP)\n",
    "cbar = fig.colorbar(sm)\n",
    "\n",
    "ax.set_xlim(Γ_min, Γ_max);\n",
    "ax.set_xlabel(r\"$\\Gamma_{i, 1}$\");\n",
    "\n",
    "ax.set_ylim(Γ_min, Γ_max);\n",
    "ax.set_ylabel(r\"$\\Gamma_{i, 2}$\");\n",
    "\n",
    "cbar.set_label(r\"$\\mathrm{tr}_i$\");\n",
    "ax.legend(loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aa170cd",
   "metadata": {},
   "source": [
    "The inclusion of the noise term $\\varepsilon^{\\Gamma}_i$ causes some of the treated units to be below the treatment threshold line in this plot.\n",
    "\n",
    "We now generate $K = 10$ covariates for each unit, one of which is a constant intercept and the rest of which follow a standard normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "42137da2",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1a665c95",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.empty((N, K))\n",
    "X[:, 0] = 1.\n",
    "X[:, 1:] = rng.normal(size=(N, K - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5668936a",
   "metadata": {},
   "source": [
    "Following the paper, the first $K_* = 4$ covariates influence the outcome, and the rest are uncorrelated with it.  The true regression coefficients, $B_j$ are taken from the BASC-CCS paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a7591803",
   "metadata": {},
   "outputs": [],
   "source": [
    "K_star = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1c2964e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.zeros(K)\n",
    "B[:K_star] = 3., 6., 4., 2."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8111d17b",
   "metadata": {},
   "source": [
    "The influence of each of the first $K_*$ covariates varies by unit, according to $A_{i, j} \\sim N\\left(0, \\left(\\frac{B_j}{2}\\right)^2\\right)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "686f12ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.zeros((N, K))\n",
    "A[:, :K_star] = rng.normal(0., 0.25 * B[:K_star]**2, size=(N, K_star))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5454063",
   "metadata": {},
   "source": [
    "The influence of these first $K_*$ covariates also varies over time according to an $AR(1)$ process $\\Xi_{j, t}$ with autocorrelation of $0.6$ and standard normal innovations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "78e0815d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ar1(k, innov):\n",
    "    t = np.arange(innov.shape[-1])\n",
    "    expon = sp.linalg.toeplitz(t)\n",
    "        \n",
    "    return np.dot(innov, np.triu(np.power(k, expon)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "09e03dac",
   "metadata": {},
   "outputs": [],
   "source": [
    "innov_Ξ = rng.normal(size=(K_star, T))\n",
    "\n",
    "Ξ = np.zeros((K, T))\n",
    "Ξ[:K_star] = ar1(0.6, innov_Ξ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "29ace990",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(t, Ξ.T, c='k', alpha=0.75);\n",
    "\n",
    "ax.set_xlabel(\"$t$\");\n",
    "ax.set_ylabel(r\"$\\Xi_{i, t}$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d708f976",
   "metadata": {},
   "source": [
    "The horizontal lines at zero here correspond to the $K - K_*$ covariates that have no influence on the outcome and do not vary over time.\n",
    "\n",
    "The noise in outcomes is related to the latent parameters $\\Gamma_i$ through factor loadings $F_t$, which also follow an $AR(1)$ process with autocorrelation of $0.7$ and standard normal innovations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f955e300",
   "metadata": {},
   "outputs": [],
   "source": [
    "innov_F = rng.normal(size=(2, T))\n",
    "\n",
    "F = ar1(0.7, innov_F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3c397ab2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(t, F.T, c='k', alpha=0.75);\n",
    "\n",
    "ax.set_xlabel(\"$t$\");\n",
    "ax.set_ylabel(r\"$F_{i, t}$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3eabb25",
   "metadata": {},
   "source": [
    "Finally, we simulate the treament effects, which are\n",
    "\n",
    "$$\n",
    "\\Delta_{i, t} =\n",
    "    \\begin{cases}\n",
    "        t - T_{\\mathrm{treat}} + \\varepsilon^{\\mathrm{treat}}_{i, t} & \\mathrm{if}\\ t > T_{\\mathrm{treat}} \\\\\n",
    "        0 & \\mathrm{if}\\ t \\leq T_{\\mathrm{treat}}\n",
    "    \\end{cases}\n",
    "$$\n",
    "\n",
    "where $\\varepsilon^{\\mathrm{treat}}_{i, t} \\sim N(0, 2^{-2})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9723d1c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Δ = np.zeros((N, T))\n",
    "Δ[:, T_treat:] = t[T_treat:] - T_treat + rng.normal(0., 0.25, size=(N, T - T_treat))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a1848b8",
   "metadata": {},
   "source": [
    "The array `w` indicates which units where treated at a given time, with\n",
    "\n",
    "$$\n",
    "w_{i, t} =\n",
    "    \\begin{cases}\n",
    "        1 & \\mathrm{if\\ unit}\\ i\\ \\mathrm{is\\ treated\\ at\\ time}\\ t \\\\\n",
    "        0 & \\mathrm{otherwise}\n",
    "    \\end{cases}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "376f83c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.zeros((N, T))\n",
    "w[treated, T_treat:] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4f10d5f",
   "metadata": {},
   "source": [
    "We plot the treatment effects that our model will attempt to recover."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "76148293",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(t, (Δ * w)[~treated][0],\n",
    "        c='k', label=\"Untreated\");\n",
    "ax.plot(t, (Δ * w)[treated][0],\n",
    "        c='r', alpha=0.75,\n",
    "        label=\"Treated\");\n",
    "ax.plot(t, (Δ * w)[treated][1:].T,\n",
    "        c='r', alpha=0.75);\n",
    "\n",
    "ax.set_xlabel(\"$t$\");\n",
    "ax.set_ylabel(r\"$\\Delta_{i, t}\\ w_{i, t}$\");\n",
    "ax.legend(loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "652b7d7f",
   "metadata": {},
   "source": [
    "We combine each of these components to generate the data to be modeled."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ba96cc24",
   "metadata": {},
   "outputs": [],
   "source": [
    "Θ = (B + A)[..., np.newaxis] + Ξ[np.newaxis]\n",
    "XΘ = (X[..., np.newaxis] * Θ).sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba75312f",
   "metadata": {},
   "source": [
    "We combine the reatment effects, the effects of the covariates, the effects of the latent factors, and standard normal noise to get the observed outcomes, $y_{i, t}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b3cb440e",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = Δ * w + XΘ + Γ.dot(F) + rng.normal(size=(N, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "179dc358",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.axvline(T_treat, c='k', ls='--',\n",
    "           label=\"$T_{\\mathrm{treat}}$\");\n",
    "\n",
    "ax.plot(t, y[~treated].T, c='k', alpha=0.5);\n",
    "ax.plot([], [], c='k', alpha=0.5,\n",
    "        label=\"Untreated\");\n",
    "\n",
    "ax.plot(t, y[treated].T, c='r', lw=3, alpha=0.75);\n",
    "ax.plot([], [], c='r', alpha=0.75,\n",
    "        label=\"Treated\");\n",
    "\n",
    "ax.set_xlabel(\"$t$\");\n",
    "ax.set_ylabel(\"$y_{i, t}$\");\n",
    "ax.legend(loc=\"upper left\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cebb3136",
   "metadata": {},
   "source": [
    "We see that the treated units have outcomes that generally trend up after $T_{\\mathrm{treat}}$, but there is a lot of visual noise to interpret when comparing those to the untreated units.  Thee BASC-CCS model w will build in the next section will help to quantify the difference and cut through this noise."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46b6158c",
   "metadata": {},
   "source": [
    "## Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c999d7a",
   "metadata": {},
   "source": [
    "### Unidentified latent factors\n",
    "\n",
    "We begin with a model that has [unidentified](https://en.wikipedia.org/wiki/Identifiability#:~:text=In%20statistics%2C%20identifiability%20is%20a,number%20of%20observations%20from%20it.) latent factors in order to determine which factors we should constrain to best identify our model.  For more details about implemented identifiabile factor analysis models in PyMC see my [previous post](https://austinrochford.com/posts/2021-07-05-factor-analysis-pymc3.html) on the topic.\n",
    "\n",
    "Since we are using the Bayesian causal-inference-as-missing-data paradigm, we define the control observations as a [masked array](https://numpy.org/doc/stable/reference/maskedarray.html), with entries masked when $w_{i, t} = 1$, indicating that the $i$-th unit was treated at time $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "a923d319",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_ctrl = np.ma.array(y, mask=w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99658635",
   "metadata": {},
   "source": [
    "For simplicity our model will use two latent factors, even though in general we do not know the true number of latent factors.  For a more rigorous discussion of how to choose the number of latent factors, see [_Machine Learning, A Probabilistic Perspective_](https://probml.github.io/pml-book/)^[Murphy, Kevin P. _Machine learning: a probabilistic perspective._ MIT press, 2012.], §12.3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "914c1a40",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_factor = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf479f87",
   "metadata": {},
   "source": [
    "We define the coordinates for our parameters. (For more information on how to get PyMC3 to interact nicely with [`xarray`](http://xarray.pydata.org/en/stable/index.html) via coordinates, see Oriol Abril's excellent [post](https://oriolabril.github.io/oriol_unraveled/python/arviz/pymc3/xarray/2020/09/22/pymc3-arviz.html) on the subject.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ab220a33",
   "metadata": {},
   "outputs": [],
   "source": [
    "coords = {\n",
    "    \"unit\": np.arange(N),                        # units\n",
    "    \"fact\": np.arange(N_factor),                 # latent factors\n",
    "    \"feat\": np.arange(K),                        # features\n",
    "    \"time\": t,                                   # time\n",
    "    \"time_block\": np.arange(T - (N_factor + 1))  # block of time for identifying factors\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c393e604",
   "metadata": {},
   "source": [
    "We put centered normal priors on our shared regression coefficients, $\\beta_j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "25ca1287",
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model(coords=coords) as ref_model:\n",
    "    β = pm.Normal(\"β\", 0., 5., dims=\"feat\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5987f5c",
   "metadata": {},
   "source": [
    "We put hierarchical normally distributed priors with mean zero (for identifiability) on the per-unit random effects $\\alpha_{i, j}$ and the per-time random effects $\\xi_{j, t}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0a1f47f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the scale necessary to make a halfnormal distribution\n",
    "# have unit variance\n",
    "HALFNORMAL_SCALE = 1. / np.sqrt(1. - 2. / np.pi)\n",
    "\n",
    "def noncentered_normal(name, dims, μ=None,):\n",
    "    if μ is None:\n",
    "        μ = pm.Normal(f\"μ_{name}\", 0., 2.5)\n",
    "\n",
    "    Δ = pm.Normal(f\"Δ_{name}\", 0., 1., dims=dims)\n",
    "    σ = pm.HalfNormal(f\"σ_{name}\", 2.5 * HALFNORMAL_SCALE)\n",
    "    \n",
    "    return pm.Deterministic(name, μ + Δ * σ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c619ee7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "with ref_model:\n",
    "    α = noncentered_normal(\"α\", (\"unit\", \"feat\"), μ=0.)\n",
    "    ξ = noncentered_normal(\"ξ\", (\"feat\", \"time\"), μ=0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c65be6ac",
   "metadata": {},
   "source": [
    "Note that here we do not use the fact that the true values of $\\Xi_{j, t}$ form an AR(1) process.\n",
    "\n",
    "We combine $\\beta_j$, $\\alpha_{i, j}$, and $\\xi_{j, t}$ to form the full coefficient cube, $\\theta_{i, j, t}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "1a1096c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "θ = β[np.newaxis, :, np.newaxis] \\\n",
    "        + α[..., np.newaxis] \\\n",
    "        + ξ[np.newaxis, ...]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27078b62",
   "metadata": {},
   "source": [
    "We build latent factor component of the model as in the previous post, knowing that this model specificiation is only identified up to reflections of `f_unid` and `γ_unid`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d9e67034",
   "metadata": {},
   "outputs": [],
   "source": [
    "with ref_model:\n",
    "    f_pos_row = pm.HalfNormal(\"f_pos_row\", HALFNORMAL_SCALE,\n",
    "                              dims=\"fact\")\n",
    "    f_block_unid = pm.Normal(\"f_block_unid\", 0., 1.,\n",
    "                             dims=(\"time_block\", \"fact\"))\n",
    "    f_unid = at.concatenate((\n",
    "        at.eye(N_factor),\n",
    "        at.shape_padleft(f_pos_row),\n",
    "        f_block_unid\n",
    "    ))\n",
    "    γ_unid = pm.Normal(\"γ_unid\", 0., 1., dims=(\"unit\", \"fact\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "383304b4",
   "metadata": {},
   "source": [
    "Finally, we specify our observational model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "f65fc923",
   "metadata": {},
   "outputs": [],
   "source": [
    "with ref_model:\n",
    "    μ_ctrl = (X[..., np.newaxis] * θ).sum(axis=1) + γ_unid.dot(f_unid.T)\n",
    "    \n",
    "    σ = pm.HalfNormal(\"σ\", 2.5)\n",
    "    obs_ctrl = pm.Normal(\"obs_ctrl\", μ_ctrl, σ, observed=y_ctrl)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc467a2b",
   "metadata": {},
   "source": [
    "We now draw 100 samples from this unidentified model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "409abe9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "CORES = 3\n",
    "\n",
    "SAMPLE_KWARGS = {\n",
    "    \"cores\": CORES,\n",
    "    \"random_seed\": [SEED + i for i in range(CORES)],\n",
    "    \"return_inferencedata\": True\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "353b2835",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Only 100 samples in chain.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [β, Δ_α, σ_α, Δ_ξ, σ_ξ, f_pos_row, f_block_unid, γ_unid, σ, obs_ctrl_missing]\n"
     ]
    },
    {
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       "                border: none;\n",
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       "      100.00% [600/600 00:02<00:00 Sampling 3 chains, 54 divergences]\n",
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     "text": [
      "Sampling 3 chains for 100 tune and 100 draw iterations (300 + 300 draws total) took 3 seconds.\n",
      "There were 19 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The acceptance probability does not match the target. It is 1.0, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "There were 12 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The acceptance probability does not match the target. It is 1.0, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "There were 23 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The acceptance probability does not match the target. It is 1.0, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The rhat statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The number of effective samples is smaller than 10% for some parameters.\n"
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    "with ref_model:\n",
    "    ref_trace = pm.sample(tune=100, draws=100, **SAMPLE_KWARGS)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c4496f4e",
   "metadata": {},
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       ".xr-preview,\n",
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       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:           ()\n",
       "Data variables:\n",
       "    β                 float64 3.886\n",
       "    Δ_α               float64 3.886\n",
       "    σ_α               float64 3.886\n",
       "    Δ_ξ               float64 3.886\n",
       "    σ_ξ               float64 3.886\n",
       "    f_pos_row         float64 3.853\n",
       "    f_block_unid      float64 3.825\n",
       "    γ_unid            float64 3.871\n",
       "    σ                 float64 3.886\n",
       "    obs_ctrl_missing  float64 3.561\n",
       "    α                 float64 3.886\n",
       "    ξ                 float64 3.886</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-8558f2a2-0da5-4b79-8747-a900fd6ee96e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-8558f2a2-0da5-4b79-8747-a900fd6ee96e' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-91c74717-4451-44e6-a0eb-28b921be9d64' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-91c74717-4451-44e6-a0eb-28b921be9d64' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-4e7d3905-def2-45c7-8cc8-b5c6cfd57421' class='xr-section-summary-in' type='checkbox'  checked><label for='section-4e7d3905-def2-45c7-8cc8-b5c6cfd57421' class='xr-section-summary' >Data variables: <span>(12)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-b938761a-7d81-491d-8db0-c856a191ede1' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b938761a-7d81-491d-8db0-c856a191ede1' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-812c338d-ab0f-45a2-82b3-48587c69f8da' class='xr-var-data-in' type='checkbox'><label for='data-812c338d-ab0f-45a2-82b3-48587c69f8da' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-02f598f2-837b-4d9f-a335-3b4cac8a5fcb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-02f598f2-837b-4d9f-a335-3b4cac8a5fcb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-078135b1-fd29-4a5a-97b9-065471b3582f' class='xr-var-data-in' type='checkbox'><label for='data-078135b1-fd29-4a5a-97b9-065471b3582f' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-54a9db0d-c71f-48af-befd-108e496c9215' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-54a9db0d-c71f-48af-befd-108e496c9215' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-71e466e3-2f1f-4fc3-95d8-555f5d69fd24' class='xr-var-data-in' type='checkbox'><label for='data-71e466e3-2f1f-4fc3-95d8-555f5d69fd24' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-439fa54d-9af7-40bf-89d7-caa8a233a2e4' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-439fa54d-9af7-40bf-89d7-caa8a233a2e4' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-779870a3-60a6-4dea-9f40-842ce14f534d' class='xr-var-data-in' type='checkbox'><label for='data-779870a3-60a6-4dea-9f40-842ce14f534d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-cfb7df2d-7cf2-4c7b-9cd5-343f1aa3a421' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cfb7df2d-7cf2-4c7b-9cd5-343f1aa3a421' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-94d5a8c1-e49b-49b9-8618-4b917459884d' class='xr-var-data-in' type='checkbox'><label for='data-94d5a8c1-e49b-49b9-8618-4b917459884d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_pos_row</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.853</div><input id='attrs-89b3d288-313b-458a-b754-ad52a209f350' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-89b3d288-313b-458a-b754-ad52a209f350' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-804e5388-ae20-45e7-bde4-1455db32df09' class='xr-var-data-in' type='checkbox'><label for='data-804e5388-ae20-45e7-bde4-1455db32df09' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.85334366)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_block_unid</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.825</div><input id='attrs-fe4d9ea3-4568-4277-9839-ab743771b10a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fe4d9ea3-4568-4277-9839-ab743771b10a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-513bafe8-6a71-4259-b5e6-a5bbce6dcb80' class='xr-var-data-in' type='checkbox'><label for='data-513bafe8-6a71-4259-b5e6-a5bbce6dcb80' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.82451101)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>γ_unid</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.871</div><input id='attrs-ccbc5790-dd6f-44d5-b98d-680295721afd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ccbc5790-dd6f-44d5-b98d-680295721afd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d8728cb7-8a4f-484a-badc-0cc704c1e18e' class='xr-var-data-in' type='checkbox'><label for='data-d8728cb7-8a4f-484a-badc-0cc704c1e18e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.87147037)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-8717d81e-e61f-40aa-88bb-7d5e42068f04' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8717d81e-e61f-40aa-88bb-7d5e42068f04' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2e28ff10-3c55-41df-89cd-aa4a8e65af6c' class='xr-var-data-in' type='checkbox'><label for='data-2e28ff10-3c55-41df-89cd-aa4a8e65af6c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>obs_ctrl_missing</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.561</div><input id='attrs-11767167-9776-41d4-9d4b-94cce5b223bb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-11767167-9776-41d4-9d4b-94cce5b223bb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ce3063d9-1e90-4f17-99fa-f4aad9111d76' class='xr-var-data-in' type='checkbox'><label for='data-ce3063d9-1e90-4f17-99fa-f4aad9111d76' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.560552)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-c38ce27e-8540-41e9-aa62-ee8efd8599d5' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c38ce27e-8540-41e9-aa62-ee8efd8599d5' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b820f237-f777-4e63-b66b-dafdcc11a161' class='xr-var-data-in' type='checkbox'><label for='data-b820f237-f777-4e63-b66b-dafdcc11a161' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.886</div><input id='attrs-b497e5d9-3d40-4b16-9be3-cc851e1e7c56' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b497e5d9-3d40-4b16-9be3-cc851e1e7c56' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-dadd6953-3a6b-43e1-9e67-c6e299b55fee' class='xr-var-data-in' type='checkbox'><label for='data-dadd6953-3a6b-43e1-9e67-c6e299b55fee' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(3.8857448)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2a48da80-1a4d-47fc-8b66-5f8d10d21feb' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-2a48da80-1a4d-47fc-8b66-5f8d10d21feb' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:           ()\n",
       "Data variables:\n",
       "    β                 float64 3.886\n",
       "    Δ_α               float64 3.886\n",
       "    σ_α               float64 3.886\n",
       "    Δ_ξ               float64 3.886\n",
       "    σ_ξ               float64 3.886\n",
       "    f_pos_row         float64 3.853\n",
       "    f_block_unid      float64 3.825\n",
       "    γ_unid            float64 3.871\n",
       "    σ                 float64 3.886\n",
       "    obs_ctrl_missing  float64 3.561\n",
       "    α                 float64 3.886\n",
       "    ξ                 float64 3.886"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.rhat(ref_trace).max()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b348d6c9",
   "metadata": {},
   "source": [
    "As expected, the $\\hat{R}$ parameters are quite high, indiciating that the chains have not converged well. This behavior is expected, since we know that this model is reflection-invariant and therefore has a multi-modal posterior.\n",
    "\n",
    "As in the previous post on identification in factor analysis, we choose a row of `f_block_unid` that we constrain to have all positive entries and change the signs of the entries `f_block_unid` and `γ_unid` so that they have the same relationship with the signs of this row.  We choose the row that has the chain whose latent factors have the largest posterior expected distance from the origin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "f0bbfd18",
   "metadata": {},
   "outputs": [],
   "source": [
    "sign_row = (ref_trace.posterior[\"f_block_unid\"]\n",
    "                     .mean(dim=\"draw\")\n",
    "                     .min(dim=\"fact\")\n",
    "                     .max(dim=\"chain\")\n",
    "                     .argmax()\n",
    "                     .item())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a9c0676",
   "metadata": {},
   "source": [
    "We can now specify the identified model, which is largely the same as the previous model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8c6e085a",
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model(coords=coords) as model:\n",
    "    β = pm.Normal(\"β\", 0., 5., dims=\"feat\")\n",
    "    α = noncentered_normal(\"α\", (\"unit\", \"feat\"), μ=0.)\n",
    "    ξ = noncentered_normal(\"ξ\", (\"feat\", \"time\"), μ=0.)\n",
    "    θ = β[np.newaxis, :, np.newaxis] \\\n",
    "            + α[..., np.newaxis] \\\n",
    "            + ξ[np.newaxis, ...]\n",
    "    \n",
    "    f_pos_row = pm.HalfNormal(\"f_pos_row\", HALFNORMAL_SCALE,\n",
    "                              dims=\"fact\")\n",
    "    f_block_unid = pm.Normal(\"f_block_unid\", 0., 1.,\n",
    "                             dims=(\"time_block\", \"fact\"))\n",
    "    \n",
    "    γ_unid = pm.Normal(\"γ_unid\", 0., 1., dims=(\"unit\", \"fact\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12dd9d39",
   "metadata": {},
   "source": [
    "We now enforce the sign constraints that will break the reflectional invariance of the previous model and specify the observational model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "31a117ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "with model:\n",
    "    unid_sign = at.sgn(f_block_unid[sign_row])\n",
    "    \n",
    "    f_block = pm.Deterministic(\"f_block\", unid_sign * f_block_unid,\n",
    "                               dims=(\"time_block\", \"fact\"))\n",
    "    f = at.concatenate((\n",
    "        at.eye(N_factor),\n",
    "        at.shape_padleft(f_pos_row),\n",
    "        f_block\n",
    "    ))\n",
    "    \n",
    "    γ = pm.Deterministic(\"γ\", unid_sign * γ_unid, dims=(\"unit\", \"fact\"))\n",
    "\n",
    "    μ_ctrl = (X[..., np.newaxis] * θ).sum(axis=1) + γ.dot(f.T)\n",
    "    \n",
    "    σ = pm.HalfNormal(\"σ\", 2.5)\n",
    "    obs_ctrl = pm.Normal(\"obs_ctrl\", μ_ctrl, σ, observed=y_ctrl)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d2af40e",
   "metadata": {},
   "source": [
    "We now sample from this identified model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "94df120b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [β, Δ_α, σ_α, Δ_ξ, σ_ξ, f_pos_row, f_block_unid, γ_unid, σ, obs_ctrl_missing]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 27:10<00:00 Sampling 3 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 3 chains for 1_000 tune and 1_000 draw iterations (3_000 + 3_000 draws total) took 1631 seconds.\n",
      "The rhat statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dff1227",
   "metadata": {},
   "source": [
    "For the moment we ignore the convergence warnings, because we expect the $\\hat{R}$ values for `f_block_unid` and `γ_unid` to be high.\n",
    "\n",
    "The energy plot shows no cause for concern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "33f9e8ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_energy(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2006c75e",
   "metadata": {},
   "source": [
    "Ignoring the variables we know are not identified, all of our $\\hat{R}$ statistics are reasonable as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "26fd7af0",
   "metadata": {},
   "outputs": [],
   "source": [
    "rhat_var_names = [\n",
    "    var_name for var_name in trace.posterior.data_vars\n",
    "        if not var_name.endswith(\"_unid\")\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "e9b47777",
   "metadata": {},
   "outputs": [
    {
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:           ()\n",
       "Data variables:\n",
       "    β                 float64 1.01\n",
       "    Δ_α               float64 1.013\n",
       "    σ_α               float64 1.007\n",
       "    Δ_ξ               float64 1.036\n",
       "    σ_ξ               float64 1.015\n",
       "    f_pos_row         float64 1.013\n",
       "    σ                 float64 1.001\n",
       "    obs_ctrl_missing  float64 1.011\n",
       "    α                 float64 1.013\n",
       "    ξ                 float64 1.034\n",
       "    f_block           float64 1.042\n",
       "    γ                 float64 1.056</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-65998280-3022-43da-88f8-cf34dd451bce' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-65998280-3022-43da-88f8-cf34dd451bce' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-7bd494c1-35fe-44e5-bb15-edaab60eaed3' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7bd494c1-35fe-44e5-bb15-edaab60eaed3' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-ed4def11-b9f3-4563-86ca-57cbbe99050e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-ed4def11-b9f3-4563-86ca-57cbbe99050e' class='xr-section-summary' >Data variables: <span>(12)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.01</div><input id='attrs-0469d86c-4a8a-4dc9-8b13-1b3ebb800080' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0469d86c-4a8a-4dc9-8b13-1b3ebb800080' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0ab41330-fa0d-4ecb-96ac-704b40790a85' class='xr-var-data-in' type='checkbox'><label for='data-0ab41330-fa0d-4ecb-96ac-704b40790a85' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.0098482)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.013</div><input id='attrs-0eb0cc8d-49cf-4ea3-8c84-94b2d6f54401' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0eb0cc8d-49cf-4ea3-8c84-94b2d6f54401' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ebbf2724-e7e9-464d-802c-ffcb3c89fee9' class='xr-var-data-in' type='checkbox'><label for='data-ebbf2724-e7e9-464d-802c-ffcb3c89fee9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01325675)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.007</div><input id='attrs-898ffb7c-96b6-4723-a64c-c048fc7ce1e3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-898ffb7c-96b6-4723-a64c-c048fc7ce1e3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f636c2a2-2189-4fa2-91ba-380a4ca2a56c' class='xr-var-data-in' type='checkbox'><label for='data-f636c2a2-2189-4fa2-91ba-380a4ca2a56c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.00669531)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.036</div><input id='attrs-09bed2b0-81f9-4338-8cf9-a76b6231b3f3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-09bed2b0-81f9-4338-8cf9-a76b6231b3f3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0bbdf9ad-c49e-46cc-92f5-fac68140c916' class='xr-var-data-in' type='checkbox'><label for='data-0bbdf9ad-c49e-46cc-92f5-fac68140c916' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.03648508)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.015</div><input id='attrs-b6f9e7dd-3c1b-4ce9-9d88-e7b82014887c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b6f9e7dd-3c1b-4ce9-9d88-e7b82014887c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b27c4723-5ce6-4a55-9007-390c1d1ad733' class='xr-var-data-in' type='checkbox'><label for='data-b27c4723-5ce6-4a55-9007-390c1d1ad733' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01464899)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_pos_row</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.013</div><input id='attrs-a3659e8f-a8fc-4e68-ad02-c4821eb7a36d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a3659e8f-a8fc-4e68-ad02-c4821eb7a36d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4a4ed4cb-acd5-4aa3-9995-b6d371b740c8' class='xr-var-data-in' type='checkbox'><label for='data-4a4ed4cb-acd5-4aa3-9995-b6d371b740c8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01343658)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.001</div><input id='attrs-08e55ebc-e9fc-47c8-8419-cf80a16064bd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-08e55ebc-e9fc-47c8-8419-cf80a16064bd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-60f4867e-308b-4d19-bdeb-79bda9ee5c0e' class='xr-var-data-in' type='checkbox'><label for='data-60f4867e-308b-4d19-bdeb-79bda9ee5c0e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.00105999)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>obs_ctrl_missing</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.011</div><input id='attrs-50546326-536b-4d09-a843-fd1875a264fa' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-50546326-536b-4d09-a843-fd1875a264fa' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-17ca28ea-68cb-4fea-b363-9b5d0447af62' class='xr-var-data-in' type='checkbox'><label for='data-17ca28ea-68cb-4fea-b363-9b5d0447af62' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01129683)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.013</div><input id='attrs-7140b0b7-7c3c-4fe8-923b-1cf734035e5c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7140b0b7-7c3c-4fe8-923b-1cf734035e5c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-064fef60-2949-466c-982c-c7a2da490701' class='xr-var-data-in' type='checkbox'><label for='data-064fef60-2949-466c-982c-c7a2da490701' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01336651)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.034</div><input id='attrs-4401f837-93de-4a6a-a5fc-408b5d3f74c7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4401f837-93de-4a6a-a5fc-408b5d3f74c7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5ca4535d-9bbb-45e6-a29c-5923e2bb1f57' class='xr-var-data-in' type='checkbox'><label for='data-5ca4535d-9bbb-45e6-a29c-5923e2bb1f57' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.03397122)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_block</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.042</div><input id='attrs-951f5368-d85b-46f6-9e3b-f282a66da6f7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-951f5368-d85b-46f6-9e3b-f282a66da6f7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-547d54ba-784e-4003-a934-9372cc2b1125' class='xr-var-data-in' type='checkbox'><label for='data-547d54ba-784e-4003-a934-9372cc2b1125' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.04228833)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>γ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.056</div><input id='attrs-3374aa5e-9e25-468e-ac29-91cb74e74b84' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3374aa5e-9e25-468e-ac29-91cb74e74b84' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1a1ef61c-ebe9-4cc7-b9a9-69dec1418ccb' class='xr-var-data-in' type='checkbox'><label for='data-1a1ef61c-ebe9-4cc7-b9a9-69dec1418ccb' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.05598537)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2e596d4d-1f4b-44d1-8860-89697e06c7b4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-2e596d4d-1f4b-44d1-8860-89697e06c7b4' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:           ()\n",
       "Data variables:\n",
       "    β                 float64 1.01\n",
       "    Δ_α               float64 1.013\n",
       "    σ_α               float64 1.007\n",
       "    Δ_ξ               float64 1.036\n",
       "    σ_ξ               float64 1.015\n",
       "    f_pos_row         float64 1.013\n",
       "    σ                 float64 1.001\n",
       "    obs_ctrl_missing  float64 1.011\n",
       "    α                 float64 1.013\n",
       "    ξ                 float64 1.034\n",
       "    f_block           float64 1.042\n",
       "    γ                 float64 1.056"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.rhat(trace, var_names=rhat_var_names).max()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d336a8a",
   "metadata": {},
   "source": [
    "The model has recovered the true regression coefficients reasonably well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "cd9c5b4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax, = az.plot_forest(trace, var_names=[\"β\"], combined=True)\n",
    "\n",
    "ax.scatter(B[::-1], ax.get_yticks(), c='k', zorder=5);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64ef4a1e",
   "metadata": {},
   "source": [
    "We now turn to estimating the causal effect.  First we build an array of the posterior imputed control outcomes for the treated units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "ecb664d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "post_treat_ctrl = xr.DataArray(\n",
    "    trace.posterior[\"obs_ctrl_missing\"]\n",
    "          .data\n",
    "          .reshape((CORES, 1000, n_treated, T - T_treat)),\n",
    "    dims=(\n",
    "        \"chain\", \"draw\",\n",
    "        \"treat_unit\", \"treat_time\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "550d7efb",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
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       "\n",
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       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
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       "\n",
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       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
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       "\n",
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       "\n",
       ".xr-sections {\n",
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       "\n",
       ".xr-section-item input:enabled + label {\n",
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       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
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       "\n",
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       "\n",
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       "\n",
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       "  color: var(--xr-font-color2);\n",
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       "\n",
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       "  font-size: 11px;\n",
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       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
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       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (chain: 3, draw: 5, treat_unit: 5, treat_time: 5)&gt;\n",
       "array([[[[ -5.48240855,  -1.40583986,  -1.16882855,   1.15513848,\n",
       "            2.58962206],\n",
       "         [ 13.20808896,  12.88445858,  14.36418043,  15.07695745,\n",
       "           16.34179227],\n",
       "         [ -4.30824175,  -1.50369883,   0.35375131,   5.48976743,\n",
       "            6.35838315],\n",
       "         [ -4.15231705,  -3.1699141 ,  -1.19618526,   6.06621698,\n",
       "            5.73819467],\n",
       "         [-11.98887863, -11.13130647, -12.77463059,  -5.22083523,\n",
       "           -6.70651369]],\n",
       "\n",
       "        [[ -5.62106417,  -0.24917844,  -0.60340746,   2.84949579,\n",
       "            3.60661581],\n",
       "         [ 13.72458472,  14.59830732,  15.51289501,  15.58851256,\n",
       "           17.09595773],\n",
       "         [ -1.95608378,  -1.18607989,  -1.17175732,   4.69606267,\n",
       "            6.59267873],\n",
       "         [ -5.99545929,  -2.55100091,   0.89877365,   5.88365558,\n",
       "            4.19817916],\n",
       "         [-13.19412638, -11.51276773, -11.61343367,  -4.33640092,\n",
       "...\n",
       "            3.72887305],\n",
       "         [ 11.8208942 ,  14.75091372,  14.23772572,  14.4094516 ,\n",
       "           16.36835434],\n",
       "         [ -4.71931108,  -1.41445792,  -0.79547448,   0.34267217,\n",
       "            6.31854545],\n",
       "         [ -1.89746734,  -2.21925517,   0.40691972,   1.43846017,\n",
       "            2.44418004],\n",
       "         [-12.4525229 , -12.26779703, -10.94742787,  -3.97728135,\n",
       "           -7.63383694]],\n",
       "\n",
       "        [[ -5.31758806,  -5.9868408 ,  -0.46603968,   0.31231198,\n",
       "            2.28266478],\n",
       "         [ 11.63609936,  13.2614443 ,  13.23373767,  11.50265473,\n",
       "           16.49579188],\n",
       "         [ -4.23744126,  -1.80079861,  -0.23874193,   3.22472127,\n",
       "            6.51668109],\n",
       "         [ -1.10156373,  -3.10613146,  -0.86511452,   4.11294081,\n",
       "            3.23735659],\n",
       "         [-14.31329339, -11.04990037,  -9.6506623 ,  -7.16009211,\n",
       "           -6.03681716]]]])\n",
       "Dimensions without coordinates: chain, draw, treat_unit, treat_time</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span>chain</span>: 3</li><li><span>draw</span>: 5</li><li><span>treat_unit</span>: 5</li><li><span>treat_time</span>: 5</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-dcf091e4-13ec-4f9f-bdeb-fcbaa7b83a01' class='xr-array-in' type='checkbox' checked><label for='section-dcf091e4-13ec-4f9f-bdeb-fcbaa7b83a01' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-5.482 -1.406 -1.169 1.155 2.59 ... -14.31 -11.05 -9.651 -7.16 -6.037</span></div><div class='xr-array-data'><pre>array([[[[ -5.48240855,  -1.40583986,  -1.16882855,   1.15513848,\n",
       "            2.58962206],\n",
       "         [ 13.20808896,  12.88445858,  14.36418043,  15.07695745,\n",
       "           16.34179227],\n",
       "         [ -4.30824175,  -1.50369883,   0.35375131,   5.48976743,\n",
       "            6.35838315],\n",
       "         [ -4.15231705,  -3.1699141 ,  -1.19618526,   6.06621698,\n",
       "            5.73819467],\n",
       "         [-11.98887863, -11.13130647, -12.77463059,  -5.22083523,\n",
       "           -6.70651369]],\n",
       "\n",
       "        [[ -5.62106417,  -0.24917844,  -0.60340746,   2.84949579,\n",
       "            3.60661581],\n",
       "         [ 13.72458472,  14.59830732,  15.51289501,  15.58851256,\n",
       "           17.09595773],\n",
       "         [ -1.95608378,  -1.18607989,  -1.17175732,   4.69606267,\n",
       "            6.59267873],\n",
       "         [ -5.99545929,  -2.55100091,   0.89877365,   5.88365558,\n",
       "            4.19817916],\n",
       "         [-13.19412638, -11.51276773, -11.61343367,  -4.33640092,\n",
       "...\n",
       "            3.72887305],\n",
       "         [ 11.8208942 ,  14.75091372,  14.23772572,  14.4094516 ,\n",
       "           16.36835434],\n",
       "         [ -4.71931108,  -1.41445792,  -0.79547448,   0.34267217,\n",
       "            6.31854545],\n",
       "         [ -1.89746734,  -2.21925517,   0.40691972,   1.43846017,\n",
       "            2.44418004],\n",
       "         [-12.4525229 , -12.26779703, -10.94742787,  -3.97728135,\n",
       "           -7.63383694]],\n",
       "\n",
       "        [[ -5.31758806,  -5.9868408 ,  -0.46603968,   0.31231198,\n",
       "            2.28266478],\n",
       "         [ 11.63609936,  13.2614443 ,  13.23373767,  11.50265473,\n",
       "           16.49579188],\n",
       "         [ -4.23744126,  -1.80079861,  -0.23874193,   3.22472127,\n",
       "            6.51668109],\n",
       "         [ -1.10156373,  -3.10613146,  -0.86511452,   4.11294081,\n",
       "            3.23735659],\n",
       "         [-14.31329339, -11.04990037,  -9.6506623 ,  -7.16009211,\n",
       "           -6.03681716]]]])</pre></div></div></li><li class='xr-section-item'><input id='section-b13e36de-6402-4815-83d6-be32c07a5148' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b13e36de-6402-4815-83d6-be32c07a5148' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-f7d72086-72ad-4d3a-838e-3ce876878c8d' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f7d72086-72ad-4d3a-838e-3ce876878c8d' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (chain: 3, draw: 5, treat_unit: 5, treat_time: 5)>\n",
       "array([[[[ -5.48240855,  -1.40583986,  -1.16882855,   1.15513848,\n",
       "            2.58962206],\n",
       "         [ 13.20808896,  12.88445858,  14.36418043,  15.07695745,\n",
       "           16.34179227],\n",
       "         [ -4.30824175,  -1.50369883,   0.35375131,   5.48976743,\n",
       "            6.35838315],\n",
       "         [ -4.15231705,  -3.1699141 ,  -1.19618526,   6.06621698,\n",
       "            5.73819467],\n",
       "         [-11.98887863, -11.13130647, -12.77463059,  -5.22083523,\n",
       "           -6.70651369]],\n",
       "\n",
       "        [[ -5.62106417,  -0.24917844,  -0.60340746,   2.84949579,\n",
       "            3.60661581],\n",
       "         [ 13.72458472,  14.59830732,  15.51289501,  15.58851256,\n",
       "           17.09595773],\n",
       "         [ -1.95608378,  -1.18607989,  -1.17175732,   4.69606267,\n",
       "            6.59267873],\n",
       "         [ -5.99545929,  -2.55100091,   0.89877365,   5.88365558,\n",
       "            4.19817916],\n",
       "         [-13.19412638, -11.51276773, -11.61343367,  -4.33640092,\n",
       "...\n",
       "            3.72887305],\n",
       "         [ 11.8208942 ,  14.75091372,  14.23772572,  14.4094516 ,\n",
       "           16.36835434],\n",
       "         [ -4.71931108,  -1.41445792,  -0.79547448,   0.34267217,\n",
       "            6.31854545],\n",
       "         [ -1.89746734,  -2.21925517,   0.40691972,   1.43846017,\n",
       "            2.44418004],\n",
       "         [-12.4525229 , -12.26779703, -10.94742787,  -3.97728135,\n",
       "           -7.63383694]],\n",
       "\n",
       "        [[ -5.31758806,  -5.9868408 ,  -0.46603968,   0.31231198,\n",
       "            2.28266478],\n",
       "         [ 11.63609936,  13.2614443 ,  13.23373767,  11.50265473,\n",
       "           16.49579188],\n",
       "         [ -4.23744126,  -1.80079861,  -0.23874193,   3.22472127,\n",
       "            6.51668109],\n",
       "         [ -1.10156373,  -3.10613146,  -0.86511452,   4.11294081,\n",
       "            3.23735659],\n",
       "         [-14.31329339, -11.04990037,  -9.6506623 ,  -7.16009211,\n",
       "           -6.03681716]]]])\n",
       "Dimensions without coordinates: chain, draw, treat_unit, treat_time"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_treat_ctrl.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "661ba770",
   "metadata": {},
   "source": [
    "We plot these against the observed treated values to visualize the treatment effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "bfbfde5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "treated_c = [f\"C{i}\" for i in range(n_treated)]\n",
    "\n",
    "ax.plot(post_treat_ctrl.mean(dim=(\"chain\", \"draw\")).T,\n",
    "        ls='--');\n",
    "ax.set_prop_cycle(None);\n",
    "ax.plot(y[treated, T_treat:].T);\n",
    "\n",
    "ax.set_xlabel(r\"$t - T_{\\mathrm{treated}}$\");\n",
    "ax.set_ylabel(\"y_{i, t}\");\n",
    "\n",
    "handles = [\n",
    "    Line2D([0], [0], c='k',\n",
    "           label=\"Treated (observed)\"),\n",
    "    Line2D([0], [0], c='k', ls='--',\n",
    "           label=\"Control (posterior expected value)\")\n",
    "]\n",
    "ax.legend(loc='upper left', handles=handles);\n",
    "\n",
    "ax.set_title(\"Treated units\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8983952f",
   "metadata": {},
   "source": [
    "Here we see that the posterior estimates of the treatment effect are quite close to the true values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "b3d80ebd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "low, high = post_treat_ctrl.quantile([0.025, 0.975],\n",
    "                                     dim=(\"chain\", \"draw\", \"treat_unit\"))\n",
    "ax.fill_between(np.arange(T - T_treat), low, high,\n",
    "                color='C0', alpha=0.25,\n",
    "                label=\"95% credible interval\");\n",
    "ax.plot([0, T - T_treat - 1], [0, T - T_treat - 1], \n",
    "        c='k', label=\"Actual\");\n",
    "ax.plot(\n",
    "    y[treated, T_treat:].T \\\n",
    "        - post_treat_ctrl.mean(dim=(\"chain\", \"draw\")).T,\n",
    "    c='C0', ls='--', alpha=0.75\n",
    ");\n",
    "\n",
    "handles, _ = ax.get_legend_handles_labels()\n",
    "handles.append(Line2D([0], [0], c='C0', alpha=0.75, ls='--',\n",
    "                      label=\"Posterior expected\"))\n",
    "ax.legend(loc='upper left', handles=handles);\n",
    "\n",
    "ax.set_xlabel(r\"$t - T_{\\mathrm{treated}}$\");\n",
    "ax.set_ylabel(\"Treatment effect\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93a65925",
   "metadata": {},
   "source": [
    "It is interesting that the 95% credibe interval is so large, probably due to the low number of treated units."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87b166d3",
   "metadata": {},
   "source": [
    "This post is available as a Jupyter notebook [here]()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3db2867d",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "9b64c7e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'./traces/draft_v0.0.2/trace.nc'"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "!mkdir -p ./traces/draft_v0.0.2/\n",
    "ref_trace.to_netcdf(\"./traces/draft_v0.0.2/ref_trace.nc\")\n",
    "trace.to_netcdf(\"./traces/draft_v0.0.2/trace.nc\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "b541d8f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "./traces/:\n",
      "total 24K\n",
      "drwxr-xr-x 2 root root 4.0K Aug  9 15:37 draft_v0.0.2\n",
      "drwxr-xr-x 2 root root 4.0K Aug  5 18:22 v0.2.0\n",
      "drwxr-xr-x 2 root root 4.0K Aug  5 19:33 v0.3.0\n",
      "drwxr-xr-x 2 root root 4.0K Aug  5 20:22 v0.3.1\n",
      "drwxr-xr-x 2 root root 4.0K Aug  6 01:31 v0.3.2\n",
      "drwxr-xr-x 2 root root 4.0K Aug  6 19:50 v0.3.3\n",
      "\n",
      "./traces/draft_v0.0.2:\n",
      "total 75M\n",
      "-rw-r--r-- 1 root root 5.8M Aug  9 15:37 ref_trace.nc\n",
      "-rw-r--r-- 1 root root  69M Aug  9 15:37 trace.nc\n",
      "\n",
      "./traces/v0.2.0:\n",
      "total 134M\n",
      "-rw-r--r-- 1 root root 69M Aug  5 18:22 id.nc\n",
      "-rw-r--r-- 1 root root 65M Aug  5 16:52 unid.nc\n",
      "\n",
      "./traces/v0.3.0:\n",
      "total 64M\n",
      "-rw-r--r-- 1 root root 64M Aug  5 19:33 trace.nc\n",
      "\n",
      "./traces/v0.3.1:\n",
      "total 69M\n",
      "-rw-r--r-- 1 root root 69M Aug  5 20:22 trace.nc\n",
      "\n",
      "./traces/v0.3.2:\n",
      "total 69M\n",
      "-rw-r--r-- 1 root root 69M Aug  6 12:01 trace.nc\n",
      "\n",
      "./traces/v0.3.3:\n",
      "total 69M\n",
      "-rw-r--r-- 1 root root 69M Aug  6 19:50 trace.nc\n"
     ]
    }
   ],
   "source": [
    "!ls -lhR ./traces/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5466a83f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
"                     .max(dim=\"chain\")\n",
    "                     .argmax()\n",
    "                     .item())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a9c0676",
   "metadata": {},
   "source": [
    "We can now specify the identified model, which is largely the same as the previous model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8c6e085a",
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model(coords=coords) as model:\n",
    "    β = pm.Normal(\"β\", 0., 5., dims=\"feat\")\n",
    "    α = noncentered_normal(\"α\", (\"unit\", \"feat\"), μ=0.)\n",
    "    ξ = noncentered_normal(\"ξ\", (\"feat\", \"time\"), μ=0.)\n",
    "    θ = β[np.newaxis, :, np.newaxis] \\\n",
    "            + α[..., np.newaxis] \\\n",
    "            + ξ[np.newaxis, ...]\n",
    "    \n",
    "    f_pos_row = pm.HalfNormal(\"f_pos_row\", HALFNORMAL_SCALE,\n",
    "                              dims=\"fact\")\n",
    "    f_block_unid = pm.Normal(\"f_block_unid\", 0., 1.,\n",
    "                             dims=(\"time_block\", \"fact\"))\n",
    "    \n",
    "    γ_unid = pm.Normal(\"γ_unid\", 0., 1., dims=(\"unit\", \"fact\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12dd9d39",
   "metadata": {},
   "source": [
    "We now enforce the sign constraints that will break the reflectional invariance of the previous model and specify the observational model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "31a117ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "with model:\n",
    "    unid_sign = at.sgn(f_block_unid[sign_row])\n",
    "    \n",
    "    f_block = pm.Deterministic(\"f_block\", unid_sign * f_block_unid,\n",
    "                               dims=(\"time_block\", \"fact\"))\n",
    "    f = at.concatenate((\n",
    "        at.eye(N_factor),\n",
    "        at.shape_padleft(f_pos_row),\n",
    "        f_block\n",
    "    ))\n",
    "    \n",
    "    γ = pm.Deterministic(\"γ\", unid_sign * γ_unid, dims=(\"unit\", \"fact\"))\n",
    "\n",
    "    μ_ctrl = (X[..., np.newaxis] * θ).sum(axis=1) + γ.dot(f.T)\n",
    "    \n",
    "    σ = pm.HalfNormal(\"σ\", 2.5)\n",
    "    obs_ctrl = pm.Normal(\"obs_ctrl\", μ_ctrl, σ, observed=y_ctrl)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d2af40e",
   "metadata": {},
   "source": [
    "We now sample from this identified model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "94df120b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [β, Δ_α, σ_α, Δ_ξ, σ_ξ, f_pos_row, f_block_unid, γ_unid, σ, obs_ctrl_missing]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 27:10<00:00 Sampling 3 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 3 chains for 1_000 tune and 1_000 draw iterations (3_000 + 3_000 draws total) took 1631 seconds.\n",
      "The rhat statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dff1227",
   "metadata": {},
   "source": [
    "For the moment we ignore the convergence warnings, because we expect the $\\hat{R}$ values for `f_block_unid` and `γ_unid` to be high.\n",
    "\n",
    "The energy plot shows no cause for concern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "33f9e8ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_energy(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2006c75e",
   "metadata": {},
   "source": [
    "Ignoring the variables we know are not identified, all of our $\\hat{R}$ statistics are reasonable as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "26fd7af0",
   "metadata": {},
   "outputs": [],
   "source": [
    "rhat_var_names = [\n",
    "    var_name for var_name in trace.posterior.data_vars\n",
    "        if not var_name.endswith(\"_unid\")\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "e9b47777",
   "metadata": {},
   "outputs": [
    {
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:           ()\n",
       "Data variables:\n",
       "    β                 float64 1.01\n",
       "    Δ_α               float64 1.013\n",
       "    σ_α               float64 1.007\n",
       "    Δ_ξ               float64 1.036\n",
       "    σ_ξ               float64 1.015\n",
       "    f_pos_row         float64 1.013\n",
       "    σ                 float64 1.001\n",
       "    obs_ctrl_missing  float64 1.011\n",
       "    α                 float64 1.013\n",
       "    ξ                 float64 1.034\n",
       "    f_block           float64 1.042\n",
       "    γ                 float64 1.056</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-65998280-3022-43da-88f8-cf34dd451bce' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-65998280-3022-43da-88f8-cf34dd451bce' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-7bd494c1-35fe-44e5-bb15-edaab60eaed3' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7bd494c1-35fe-44e5-bb15-edaab60eaed3' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-ed4def11-b9f3-4563-86ca-57cbbe99050e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-ed4def11-b9f3-4563-86ca-57cbbe99050e' class='xr-section-summary' >Data variables: <span>(12)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.01</div><input id='attrs-0469d86c-4a8a-4dc9-8b13-1b3ebb800080' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0469d86c-4a8a-4dc9-8b13-1b3ebb800080' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0ab41330-fa0d-4ecb-96ac-704b40790a85' class='xr-var-data-in' type='checkbox'><label for='data-0ab41330-fa0d-4ecb-96ac-704b40790a85' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.0098482)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.013</div><input id='attrs-0eb0cc8d-49cf-4ea3-8c84-94b2d6f54401' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0eb0cc8d-49cf-4ea3-8c84-94b2d6f54401' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ebbf2724-e7e9-464d-802c-ffcb3c89fee9' class='xr-var-data-in' type='checkbox'><label for='data-ebbf2724-e7e9-464d-802c-ffcb3c89fee9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01325675)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.007</div><input id='attrs-898ffb7c-96b6-4723-a64c-c048fc7ce1e3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-898ffb7c-96b6-4723-a64c-c048fc7ce1e3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f636c2a2-2189-4fa2-91ba-380a4ca2a56c' class='xr-var-data-in' type='checkbox'><label for='data-f636c2a2-2189-4fa2-91ba-380a4ca2a56c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.00669531)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.036</div><input id='attrs-09bed2b0-81f9-4338-8cf9-a76b6231b3f3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-09bed2b0-81f9-4338-8cf9-a76b6231b3f3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0bbdf9ad-c49e-46cc-92f5-fac68140c916' class='xr-var-data-in' type='checkbox'><label for='data-0bbdf9ad-c49e-46cc-92f5-fac68140c916' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.03648508)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.015</div><input id='attrs-b6f9e7dd-3c1b-4ce9-9d88-e7b82014887c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b6f9e7dd-3c1b-4ce9-9d88-e7b82014887c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b27c4723-5ce6-4a55-9007-390c1d1ad733' class='xr-var-data-in' type='checkbox'><label for='data-b27c4723-5ce6-4a55-9007-390c1d1ad733' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01464899)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_pos_row</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.013</div><input id='attrs-a3659e8f-a8fc-4e68-ad02-c4821eb7a36d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a3659e8f-a8fc-4e68-ad02-c4821eb7a36d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4a4ed4cb-acd5-4aa3-9995-b6d371b740c8' class='xr-var-data-in' type='checkbox'><label for='data-4a4ed4cb-acd5-4aa3-9995-b6d371b740c8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01343658)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.001</div><input id='attrs-08e55ebc-e9fc-47c8-8419-cf80a16064bd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-08e55ebc-e9fc-47c8-8419-cf80a16064bd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-60f4867e-308b-4d19-bdeb-79bda9ee5c0e' class='xr-var-data-in' type='checkbox'><label for='data-60f4867e-308b-4d19-bdeb-79bda9ee5c0e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.00105999)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>obs_ctrl_missing</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.011</div><input id='attrs-50546326-536b-4d09-a843-fd1875a264fa' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-50546326-536b-4d09-a843-fd1875a264fa' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-17ca28ea-68cb-4fea-b363-9b5d0447af62' class='xr-var-data-in' type='checkbox'><label for='data-17ca28ea-68cb-4fea-b363-9b5d0447af62' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01129683)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>α</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.013</div><input id='attrs-7140b0b7-7c3c-4fe8-923b-1cf734035e5c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7140b0b7-7c3c-4fe8-923b-1cf734035e5c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-064fef60-2949-466c-982c-c7a2da490701' class='xr-var-data-in' type='checkbox'><label for='data-064fef60-2949-466c-982c-c7a2da490701' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.01336651)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>ξ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.034</div><input id='attrs-4401f837-93de-4a6a-a5fc-408b5d3f74c7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4401f837-93de-4a6a-a5fc-408b5d3f74c7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5ca4535d-9bbb-45e6-a29c-5923e2bb1f57' class='xr-var-data-in' type='checkbox'><label for='data-5ca4535d-9bbb-45e6-a29c-5923e2bb1f57' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.03397122)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>f_block</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.042</div><input id='attrs-951f5368-d85b-46f6-9e3b-f282a66da6f7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-951f5368-d85b-46f6-9e3b-f282a66da6f7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-547d54ba-784e-4003-a934-9372cc2b1125' class='xr-var-data-in' type='checkbox'><label for='data-547d54ba-784e-4003-a934-9372cc2b1125' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.04228833)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>γ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.056</div><input id='attrs-3374aa5e-9e25-468e-ac29-91cb74e74b84' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3374aa5e-9e25-468e-ac29-91cb74e74b84' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1a1ef61c-ebe9-4cc7-b9a9-69dec1418ccb' class='xr-var-data-in' type='checkbox'><label for='data-1a1ef61c-ebe9-4cc7-b9a9-69dec1418ccb' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.05598537)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2e596d4d-1f4b-44d1-8860-89697e06c7b4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-2e596d4d-1f4b-44d1-8860-89697e06c7b4' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:           ()\n",
       "Data variables:\n",
       "    β                 float64 1.01\n",
       "    Δ_α               float64 1.013\n",
       "    σ_α               float64 1.007\n",
       "    Δ_ξ               float64 1.036\n",
       "    σ_ξ               float64 1.015\n",
       "    f_pos_row         float64 1.013\n",
       "    σ                 float64 1.001\n",
       "    obs_ctrl_missing  float64 1.011\n",
       "    α                 float64 1.013\n",
       "    ξ                 float64 1.034\n",
       "    f_block           float64 1.042\n",
       "    γ                 float64 1.056"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.rhat(trace, var_names=rhat_var_names).max()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d336a8a",
   "metadata": {},
   "source": [
    "The model has recovered the true regression coefficients reasonably well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "cd9c5b4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax, = az.plot_forest(trace, var_names=[\"β\"], combined=True)\n",
    "\n",
    "ax.scatter(B[::-1], ax.get_yticks(), c='k', zorder=5);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64ef4a1e",
   "metadata": {},
   "source": [
    "We now turn to estimating the causal effect.  First we build an array of the posterior imputed control outcomes for the treated units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "ecb664d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "post_treat_ctrl = xr.DataArray(\n",
    "    trace.posterior[\"obs_ctrl_missing\"]\n",
    "          .data\n",
    "          .reshape((CORES, 1000, n_treated, T - T_treat)),\n",
    "    dims=(\n",
    "        \"chain\", \"draw\",\n",
    "        \"treat_unit\", \"treat_time\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "550d7efb",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
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       "\n",
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       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
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       "\n",
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       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
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       "\n",
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       "\n",
       ".xr-sections {\n",
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       "\n",
       ".xr-section-item input:enabled + label {\n",
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       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
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       "\n",
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       "\n",
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       "\n",
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       "  color: var(--xr-font-color2);\n",
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       "\n",
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       "  font-size: 11px;\n",
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       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
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       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (chain: 3, draw: 5, treat_unit: 5, treat_time: 5)&gt;\n",
       "array([[[[ -5.48240855,  -1.40583986,  -1.16882855,   1.15513848,\n",
       "            2.58962206],\n",
       "         [ 13.20808896,  12.88445858,  14.36418043,  15.07695745,\n",
       "           16.34179227],\n",
       "         [ -4.30824175,  -1.50369883,   0.35375131,   5.48976743,\n",
       "            6.35838315],\n",
       "         [ -4.15231705,  -3.1699141 ,  -1.19618526,   6.06621698,\n",
       "            5.73819467],\n",
       "         [-11.98887863, -11.13130647, -12.77463059,  -5.22083523,\n",
       "           -6.70651369]],\n",
       "\n",
       "        [[ -5.62106417,  -0.24917844,  -0.60340746,   2.84949579,\n",
       "            3.60661581],\n",
       "         [ 13.72458472,  14.59830732,  15.51289501,  15.58851256,\n",
       "           17.09595773],\n",
       "         [ -1.95608378,  -1.18607989,  -1.17175732,   4.69606267,\n",
       "            6.59267873],\n",
       "         [ -5.99545929,  -2.55100091,   0.89877365,   5.88365558,\n",
       "            4.19817916],\n",
       "         [-13.19412638, -11.51276773, -11.61343367,  -4.33640092,\n",
       "...\n",
       "            3.72887305],\n",
       "         [ 11.8208942 ,  14.75091372,  14.23772572,  14.4094516 ,\n",
       "           16.36835434],\n",
       "         [ -4.71931108,  -1.41445792,  -0.79547448,   0.34267217,\n",
       "            6.31854545],\n",
       "         [ -1.89746734,  -2.21925517,   0.40691972,   1.43846017,\n",
       "            2.44418004],\n",
       "         [-12.4525229 , -12.26779703, -10.94742787,  -3.97728135,\n",
       "           -7.63383694]],\n",
       "\n",
       "        [[ -5.31758806,  -5.9868408 ,  -0.46603968,   0.31231198,\n",
       "            2.28266478],\n",
       "         [ 11.63609936,  13.2614443 ,  13.23373767,  11.50265473,\n",
       "           16.49579188],\n",
       "         [ -4.23744126,  -1.80079861,  -0.23874193,   3.22472127,\n",
       "            6.51668109],\n",
       "         [ -1.10156373,  -3.10613146,  -0.86511452,   4.11294081,\n",
       "            3.23735659],\n",
       "         [-14.31329339, -11.04990037,  -9.6506623 ,  -7.16009211,\n",
       "           -6.03681716]]]])\n",
       "Dimensions without coordinates: chain, draw, treat_unit, treat_time</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span>chain</span>: 3</li><li><span>draw</span>: 5</li><li><span>treat_unit</span>: 5</li><li><span>treat_time</span>: 5</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-dcf091e4-13ec-4f9f-bdeb-fcbaa7b83a01' class='xr-array-in' type='checkbox' checked><label for='section-dcf091e4-13ec-4f9f-bdeb-fcbaa7b83a01' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-5.482 -1.406 -1.169 1.155 2.59 ... -14.31 -11.05 -9.651 -7.16 -6.037</span></div><div class='xr-array-data'><pre>array([[[[ -5.48240855,  -1.40583986,  -1.16882855,   1.15513848,\n",
       "            2.58962206],\n",
       "         [ 13.20808896,  12.88445858,  14.36418043,  15.07695745,\n",
       "           16.34179227],\n",
       "         [ -4.30824175,  -1.50369883,   0.35375131,   5.48976743,\n",
       "            6.35838315],\n",
       "         [ -4.15231705,  -3.1699141 ,  -1.19618526,   6.06621698,\n",
       "            5.73819467],\n",
       "         [-11.98887863, -11.13130647, -12.77463059,  -5.22083523,\n",
       "           -6.70651369]],\n",
       "\n",
       "        [[ -5.62106417,  -0.24917844,  -0.60340746,   2.84949579,\n",
       "            3.60661581],\n",
       "         [ 13.72458472,  14.59830732,  15.51289501,  15.58851256,\n",
       "           17.09595773],\n",
       "         [ -1.95608378,  -1.18607989,  -1.17175732,   4.69606267,\n",
       "            6.59267873],\n",
       "         [ -5.99545929,  -2.55100091,   0.89877365,   5.88365558,\n",
       "            4.19817916],\n",
       "         [-13.19412638, -11.51276773, -11.61343367,  -4.33640092,\n",
       "...\n",
       "            3.72887305],\n",
       "         [ 11.8208942 ,  14.75091372,  14.23772572,  14.4094516 ,\n",
       "           16.36835434],\n",
       "         [ -4.71931108,  -1.41445792,  -0.79547448,   0.34267217,\n",
       "            6.31854545],\n",
       "         [ -1.89746734,  -2.21925517,   0.40691972,   1.43846017,\n",
       "            2.44418004],\n",
       "         [-12.4525229 , -12.26779703, -10.94742787,  -3.97728135,\n",
       "           -7.63383694]],\n",
       "\n",
       "        [[ -5.31758806,  -5.9868408 ,  -0.46603968,   0.31231198,\n",
       "            2.28266478],\n",
       "         [ 11.63609936,  13.2614443 ,  13.23373767,  11.50265473,\n",
       "           16.49579188],\n",
       "         [ -4.23744126,  -1.80079861,  -0.23874193,   3.22472127,\n",
       "            6.51668109],\n",
       "         [ -1.10156373,  -3.10613146,  -0.86511452,   4.11294081,\n",
       "            3.23735659],\n",
       "         [-14.31329339, -11.04990037,  -9.6506623 ,  -7.16009211,\n",
       "           -6.03681716]]]])</pre></div></div></li><li class='xr-section-item'><input id='section-b13e36de-6402-4815-83d6-be32c07a5148' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b13e36de-6402-4815-83d6-be32c07a5148' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-f7d72086-72ad-4d3a-838e-3ce876878c8d' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f7d72086-72ad-4d3a-838e-3ce876878c8d' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.DataArray (chain: 3, draw: 5, treat_unit: 5, treat_time: 5)>\n",
       "array([[[[ -5.48240855,  -1.40583986,  -1.16882855,   1.15513848,\n",
       "            2.58962206],\n",
       "         [ 13.20808896,  12.88445858,  14.36418043,  15.07695745,\n",
       "           16.34179227],\n",
       "         [ -4.30824175,  -1.50369883,   0.35375131,   5.48976743,\n",
       "            6.35838315],\n",
       "         [ -4.15231705,  -3.1699141 ,  -1.19618526,   6.06621698,\n",
       "            5.73819467],\n",
       "         [-11.98887863, -11.13130647, -12.77463059,  -5.22083523,\n",
       "           -6.70651369]],\n",
       "\n",
       "        [[ -5.62106417,  -0.24917844,  -0.60340746,   2.84949579,\n",
       "            3.60661581],\n",
       "         [ 13.72458472,  14.59830732,  15.51289501,  15.58851256,\n",
       "           17.09595773],\n",
       "         [ -1.95608378,  -1.18607989,  -1.17175732,   4.69606267,\n",
       "            6.59267873],\n",
       "         [ -5.99545929,  -2.55100091,   0.89877365,   5.88365558,\n",
       "            4.19817916],\n",
       "         [-13.19412638, -11.51276773, -11.61343367,  -4.33640092,\n",
       "...\n",
       "            3.72887305],\n",
       "         [ 11.8208942 ,  14.75091372,  14.23772572,  14.4094516 ,\n",
       "           16.36835434],\n",
       "         [ -4.71931108,  -1.41445792,  -0.79547448,   0.34267217,\n",
       "            6.31854545],\n",
       "         [ -1.89746734,  -2.21925517,   0.40691972,   1.43846017,\n",
       "            2.44418004],\n",
       "         [-12.4525229 , -12.26779703, -10.94742787,  -3.97728135,\n",
       "           -7.63383694]],\n",
       "\n",
       "        [[ -5.31758806,  -5.9868408 ,  -0.46603968,   0.31231198,\n",
       "            2.28266478],\n",
       "         [ 11.63609936,  13.2614443 ,  13.23373767,  11.50265473,\n",
       "           16.49579188],\n",
       "         [ -4.23744126,  -1.80079861,  -0.23874193,   3.22472127,\n",
       "            6.51668109],\n",
       "         [ -1.10156373,  -3.10613146,  -0.86511452,   4.11294081,\n",
       "            3.23735659],\n",
       "         [-14.31329339, -11.04990037,  -9.6506623 ,  -7.16009211,\n",
       "           -6.03681716]]]])\n",
       "Dimensions without coordinates: chain, draw, treat_unit, treat_time"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "post_treat_ctrl.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "661ba770",
   "metadata": {},
   "source": [
    "We plot these against the observed treated values to visualize the treatment effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "bfbfde5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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