Skip to content

Instantly share code, notes, and snippets.

@AustinRochford

AustinRochford/spline_heterosked.ipynb

Last active August 11, 2021 22:33
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save AustinRochford/2b7a0f79457dc6b593309db433ecbedd to your computer and use it in GitHub Desktop.
Save AustinRochford/2b7a0f79457dc6b593309db433ecbedd to your computer and use it in GitHub Desktop.
Download ZIP
Bayesian Splines with Heteroskedastic Noise in Python with PyMC3
Display the source blob
Display the rendered blob
Raw
spline_heterosked.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "41b09fcf",
"metadata": {},
"source": [
"---\n",
"title: Bayesian Splines with Heteroskedastic Noise in Python with PyMC3\n",
"tags: Bayesian Statistics, Spines, Python, PyMC3\n",
"---"
]
},
{
"cell_type": "markdown",
"id": "07a48999",
"metadata": {},
"source": [
"[Splines](https://en.wikipedia.org/wiki/Spline_(mathematics)) are a powerful tool when modeling nonlinear relationships. This post shows how to include splines in a Bayesian model in Python using [`pymc3`](https://en.wikipedia.org/wiki/Spline_(mathematics)). In addition, we will show how to use a second spline component to handle [heteroskedastic](https://en.wikipedia.org/wiki/Heteroscedasticity) data, that is, data where the noise scale is not constant.\n",
"\n",
"<center>\n",
"<fig>\n",
"<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Cardinal_cubic_B-spline2.svg/1280px-Cardinal_cubic_B-spline2.svg.png\" width=600>\n",
"<caption>Image credit [Wikipedia](https://en.wikipedia.org/wiki/B-spline)</caption>\n",
"</fig>\n",
"</center>\n",
"\n",
"To illustrate these concepts, we will use [Lidar](https://en.wikipedia.org/wiki/Lidar) data from Larry Wasserman's excellent book [_All of Nonparametric Statistics_](http://www.stat.cmu.edu/~larry/all-of-nonpar/)."
]
},
{
"cell_type": "markdown",
"id": "ca21642c",
"metadata": {},
"source": [
"## Load the Data\n",
"\n",
"First we make the necessary Python imports and do some light housekeeping."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a3304a1a",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "c9f3e31a",
"metadata": {},
"outputs": [],
"source": [
"from warnings import filterwarnings"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "71b4fdd4",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"You are running the v4 development version of PyMC3 which currently still lacks key features. You probably want to use the stable v3 instead which you can either install via conda or find on the v3 GitHub branch: https://github.com/pymc-devs/pymc3/tree/v3\n"
]
}
],
"source": [
"from aesara import shared, tensor as at\n",
"import arviz as az\n",
"import matplotlib as mpl\n",
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import pymc3 as pm\n",
"import scipy as sp\n",
"import seaborn as sns"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "fc04d090",
"metadata": {},
"outputs": [],
"source": [
"filterwarnings('ignore', category=UserWarning, module='arviz')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "9d821892",
"metadata": {},
"outputs": [],
"source": [
"mpl.rcParams['figure.figsize'] = (8, 6)\n",
"\n",
"sns.set(color_codes=True)"
]
},
{
"cell_type": "markdown",
"id": "4d899539",
"metadata": {},
"source": [
"We are now ready to load the data."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "fa68eb8b",
"metadata": {},
"outputs": [],
"source": [
"DATA_URL = 'http://www.stat.cmu.edu/~larry/all-of-nonpar/=data/lidar.dat'"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a9197977",
"metadata": {},
"outputs": [],
"source": [
"df = pd.read_csv(DATA_URL, sep=' +', engine='python')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "7d036e5e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>range</th>\n",
" <th>logratio</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>390</td>\n",
" <td>-0.050356</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>391</td>\n",
" <td>-0.060097</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>393</td>\n",
" <td>-0.041901</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>394</td>\n",
" <td>-0.050985</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>396</td>\n",
" <td>-0.059913</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" range logratio\n",
"0 390 -0.050356\n",
"1 391 -0.060097\n",
"2 393 -0.041901\n",
"3 394 -0.050985\n",
"4 396 -0.059913"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "ff6ffd1f",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>range</th>\n",
" <th>logratio</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>221.000000</td>\n",
" <td>221.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>554.751131</td>\n",
" <td>-0.291156</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>95.912396</td>\n",
" <td>0.282475</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>390.000000</td>\n",
" <td>-0.949554</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>472.000000</td>\n",
" <td>-0.542305</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>555.000000</td>\n",
" <td>-0.108043</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>637.000000</td>\n",
" <td>-0.054825</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>720.000000</td>\n",
" <td>0.026907</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" range logratio\n",
"count 221.000000 221.000000\n",
"mean 554.751131 -0.291156\n",
"std 95.912396 0.282475\n",
"min 390.000000 -0.949554\n",
"25% 472.000000 -0.542305\n",
"50% 555.000000 -0.108043\n",
"75% 637.000000 -0.054825\n",
"max 720.000000 0.026907"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.describe()"
]
},
{
"cell_type": "markdown",
"id": "edcbf9a2",
"metadata": {},
"source": [
"We standardize both `range` and `logratio` to make it easier to specify priors once we begin building our spline models."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "9cd86700",
"metadata": {},
"outputs": [],
"source": [
"std_df = (df - df.mean()) / df.std()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "e5e9e18e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>range</th>\n",
" <th>logratio</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-1.717725</td>\n",
" <td>0.852467</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>-1.707299</td>\n",
" <td>0.817981</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>-1.686447</td>\n",
" <td>0.882398</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>-1.676020</td>\n",
" <td>0.850240</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>-1.655168</td>\n",
" <td>0.818631</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" range logratio\n",
"0 -1.717725 0.852467\n",
"1 -1.707299 0.817981\n",
"2 -1.686447 0.882398\n",
"3 -1.676020 0.850240\n",
"4 -1.655168 0.818631"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"std_df.head()"
]
},
{
"cell_type": "markdown",
"id": "77ae58b1",
"metadata": {},
"source": [
"### Exploratory Data Analysis"
]
},
{
"cell_type": "markdown",
"id": "2ec54dcf",
"metadata": {},
"source": [
"The task at hand is to model (standardized) `logratio` as a function of (standardized) `range`."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "4d72b60b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAi0AAAGhCAYAAACtc4RMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAABpxUlEQVR4nO3deZyT1dk//k/2SSaZJZnMBsM67IuggFXrRgdRHhT5tihiNxdapRTr8+gjVX8q1Fqxtdal2NpqfVqtC1WgAiKiFlsXpBYFAZFtYCCZGWZPJplMlvv3RyZhMtlnkty5M5/368WLIbmT+5wkzH3lnOtcRyYIggAiIiKiLCcXuwFEREREiWDQQkRERJLAoIWIiIgkgUELERERSQKDFiIiIpIEBi1EREQkCQxaiIiISBKUYjcgV7S2dsLnk2bJG5NJj+Zmu9jNyDj2e3BhvwcX9lua5HIZiovzo97PoCVFfD5BskELAEm3fSDY78GF/R5c2O/UsjvdeO8/J2HIV+OSaUPSco54GLQQERFRVG12F7Z9Uof3PjsFV7cXV3xtmGhtYdBCRESUhZwuD9xeHwxaFWQyWcbP39jmxNaPj+Nfe63w+gScO7EM8742HEPN+oy3JYBBCxERURZxe7x4+98nsenDWnR1e6HVKFBarENZsTb4d1mxDqVGbVoCmpONdmz5+Dh2HmiAQi7D16dW4vJzh6G0SJvS8/QHgxYiIqIsIAgC/n3wNNa9dxhN7V2YVl2C8cOL0djqQGOrE8esHdj1ZSN6b3Os1ShRWqwNBjKjhxVDIwfMRVoU6TWQyxMPaI6casfmj47js8NN0KgVmDtzGC6bVYUivSYNve0fBi1EREQiO2btwMvvHMKhk+0YatbjjsXTMHGEMew4j9eHpvYuNLQ40NDqRENPQHPU0hPQfFgbPFYhl8FUkAdTYR7MRXkwFWphLsxDSaEWJUV5KMhXQwZgf20rNn9Uiy9PtCE/T4mrvz4Ss88ZCr1WlbkXIEEMWoiIiETSanPhtR1H8OEX9SjQqfD9K8bj61Mqoo6QKBVylBt1KDfqwu5ze3wQlAp8dawJTW1daGrvQlO7E03tXfjscDM6OrvDnkuvVaLN3o0ivRqLZ1fjommVyFNnb2iQvS0jIiLKUa5uL7Z+cgJv7jwOnw+Y97Xh+K/zhkOr6f9lWaWUw2zWQ43IS55dbi+aewUyTe1daLW5MG5YES6YXAGVMvvrzWY8aPH5fCH/lsuz/0UiIqLcIwgC6lscOHyqHbVWGwRBgDZPCZ1GCa3mzN9ajRK6Xrdr1ArI+5n86hMEfLyvHq/tOIpWmwszx5fiW5eMhjkDSa4alQKVJfmoLIlevC3bxQxalixZklBW8osvvhjz/n379mH16tU4ePAgXC4XAP+HRSaT4cCBA0k0l4iIqH9cbi9qrR04fKodR075/7Y73QD8Ca1KhQxOlwceb+zibDIZoFX7A5lAcBMMavIC/1ZBq1FAp1EF77N3ufH6jiM4ZrVhRLkBP7xqEsZWFWWg57kjZtCyaNGi4M8nTpzAa6+9hoULF6KyshIWiwUbNmzAN7/5zbgnWblyJS699FI89NBDyMvLG3iriYiI4mi1uXDoZFtPkNKOEw12eHuqxZYbdZhWXYLqoYWoHlKIcpMOcpkMgiDA7fHB6fLA0fPH6fLA6fLC0eX2/+1yw9nV83fP7afbnCHHRlNs0ODm+RPwtUnl/R6tGcxiBi0LFy4M/nzNNdfg2WefxZgxY4K3XXnllbj77ruxYsWKmCc5deoUbr/99qTXkrvdbnz++ef48ssv0dHRgYKCAowfPx5nnXUWVKrEspqPHTuGlStXoq2tDUVFRVizZg1GjBgR8dijR49i4cKFWLJkCe66666k2kpERNlh91en8crvP0JjqxMAoFbKMbKiAJefOwyjhxRidGUBDDp1xMfKZDKoVQqoVQoU9nOpr88nwNntgaPL/ycQAHm8Ppw1ugQataLffRvsEs5pOXLkCIYNCy3dO3ToUBw9ejTuY+fMmYN//etfuPDCCxM6V0tLC/7whz9g/fr1KCwsxKhRo5Cfn4/Ozk785S9/QXt7OxYuXIilS5fCaAxfEtbb/fffjyVLlmDBggXYuHEj7rvvPvz5z38OO87r9eL+++9HTU1NQm0kIqLs89nhJqzd8AWGlxfgG2cPRfXQQlSV6qFUZC5/Ui6XIT9Phfy87FsyLHUJBy0zZ87EypUrcdttt6G8vBxWqxVPPfUUZsyYEfexLpcLy5cvxznnnIOSkpKQ+x555JGw46+//np861vfwsaNG1FWVhZ2f0NDA9544w18+9vfxpYtW6Ket7m5Gfv378ef/vQnAMD8+fPxs5/9DC0tLWHBzjPPPINLLrkEDocDDocjbp+IiCi7fHG0GWvX78WwMj0eWnYBHPYusZtEKZZw0PLwww9j1apVmD9/PrxeLxQKBS677DI89NBDcR9bXV2N6urqhBu1ceNGqNWRh+4AoKysDDfffDO++93vxnweq9WKsrIyKBT+oTiFQoHS0lJYrdaQoOXLL7/Ev/71L/z5z3/G2rVrE25nbyaTeHsxpILZbBC7CaJgvwcX9jt3fX7oNJ56fS+GlRXg57eej3ytCvlZWBwtE3L5/U4oaPF6vfi///s/PPzww3j00UeDIxWJLldevnx5Uo2KFbD057hY3G43/r//7//DL37xi2Bw0x/NzXbJboNuNhtw+rRN7GZkHPs9uLDfueurujb8+tXPUFqsxW3fmgJnpwt6nTrn+x2J1N9vuVwWcxAgoaBFoVDgr3/9K3784x9DLpeHTfEk4uOPP8bGjRvR2NiI0tJSXHXVVTjvvPMiHpuqpdYVFRVoaGgIjgx5vV40NjaioqIieMzp06dx4sQJ/OAHPwAAdHR0QBAE2O12/OxnP0uih0RElGmHT7XjsXWfw1SQhzsWT4+aYEu5IeHMpKuvvhovvfRSv06ybt063H777TCbzZgzZw5KS0txxx134NVXX414/KJFi/Ctb30L3/rWtzBr1izU1dVhxowZuOqqqzBjxgycPHkS5557btzzmkwmTJgwAZs2bQIAbNq0CRMmTAiZGqqsrMTOnTvx7rvv4t1338X3vvc9XHPNNQxYiIiy3DFrBx579TMU5atx53XTUZDPgCXXJZzTsmfPHrzwwgt49tlnUV5eHjISEm/E449//CP+9Kc/Yfz48cHbrrjiCqxYsQLXXHNN2PGpWmoNAA888ABWrlyJtWvXoqCgAGvWrAEALF26FCtWrMCUKVPiPgcREWWXEw02PPryZ8jPU+HO66Zn1U7ElD4JBy3XXHNNxAAjEW1tbRg9enTIbaNGjUJ7e3vcxw5kqTUAjB49GuvWrQu7/Q9/+EPE43/84x8n9LxERCSOk6ft+NXLn0GrUeB/r5sOYwGLlg4WCQctvUc/knX22Wfj4Ycfxh133AGtVguHw4Ff//rXmD59etzHDmSpNRER5RZrcyd+9dJuKBUy3HnddJRkYM8eyh5JbZjY1NSEPXv2oLW1FYJwZqXMt771rZiPW7VqFf77v/8bM2bMQGFhIdrb2zF9+nQ8+uijcc/Ze6m1x+OBUqlMeKk1ERHljoYWBx55aTcg8wcspcU6sZtEGZZw0LJ9+3bceeedGD58OA4fPozq6mocOnQIZ599dtygpbS0FC+88AKsVitOnz6N0tJSlJeXJ3TeoqIiPPbYY/D5fEkvtSYiotxwus2JR17aDa9XwF1LpqPCJN2diqn/Eg5afvOb3+Chhx7CFVdcgZkzZ2LDhg147bXXcPjw4YjHB3ZxBgCfzwfAXxQuUOE2cFsiAciRI0ewdetWNDc347777sPRo0fR3d0dkthLRES5qbm9C4/8dTe63V7ced10DDFLu5gn9V/CQxYWiwVXXHFFyG0LFy7Ehg0bIh5/zjnnBH+eOHEiJk2aFPIncFs8b775Jq6//no0NDQEz9XZ2YmHH3440aYTEZFEfVXXhode+BQOlwf/s3gahpXlbrVXii/hkRaTyYSmpiaUlJRgyJAh2L17N4qLi4MjJn1t3rw5+PM777zT7wY+8cQT+NOf/oQJEybgzTffBACMHz8eX375Zb+fk4iIspvPJ2DzR7XY8K9jMBdqseK6qRhezoBlsEt4pGXRokX49NNPAQDf//738d3vfhcLFizAddddF/H43lVnt27diiFDhoT92bZtW9zztrS0BKeBAtNNMpksoYq5REQkPa02F3718m6s/+cxnDuhDPffMJMBCwFIYqQlUOYe8FfHnTVrFpxOZ1j9lUh++9vf4qabbgq7/emnn8YNN9wQ87GTJk3Cxo0bcfXVVwdv27x5M6ZOnZpo04mISCL2HGnGs5v3w+X24oZ54/H1KRX8kkpBSS157q2ysjLuMR999BEAf9Ltxx9/HLJM+uTJk8jPj5/9fc899+Cmm27C3/72NzgcDtx00004duwYnnvuuf42nYiIsozH68PrO45i6ycnMNScj1sWTEZlCVcIUaiYQcvFF1+cUIT7j3/8I+Lt99xzDwDA5XLh7rvvDt4uk8lgNptx7733xn3u0aNH480338R7772HSy65BBUVFbjkkksSCniIiCj7NbY58fuN+3DM2oFLpw/BtbOroVYpxG4WZaGYQcsvf/nL4M979+7Fhg0b8J3vfAeVlZWwWCx44YUXQqZt+nr33XcBAP/7v/+LRx55pN+N1Gq1mDdvXr8fT0RE2emTAw34v61fApBh2dWTMWN8qdhNoiwWM2iZNWtW8OfVq1fj2WefDdZZAYCLLroIN998M2688caYJxlIwFJXV4ff/OY3OHDgABwOR8h90UZ4iIgou7ncXry0/RDe/9yC0ZUF+OFVk1iSn+JKOKelsbEROl1oyWSdToeGhoa4j7Xb7XjyySexa9eusC0A4gUed9xxB6qqqnDXXXdBq+UHmohI6k6dtuN3G/fhVFMnrvjaMCy8cBSUClY6p/gSDlpmz56NW2+9Fbfeemtw48Lf//73mD17dtzHPvDAA2hoaMCyZctw55134pe//CWeffZZzJ07N+5jDx06hJdeeoml+4mIJMrp8uDIqXZ8dbIdh+racMTSDp1Gif++9ixMHmkSu3kkIQkHLatWrcKTTz6J+++/H42NjTCbzbjiiiuwfPnyuI/94IMPsGXLFhQXF0OhUKCmpgZTpkzBLbfcgu9///sxHztz5kzs378fkydPTrSpREQkoja7C4d6ApSvTrahrtEOQQBkMmBYmQGzzx6KK84dhkK9RuymksQkHLRoNBrccccduOOOO5I+ic/ng8HgLwyk0+nQ0dEBs9mM48ePx33skCFDcNNNN+Gyyy5DSUlJyH233XZb0m0hIqLUEQQBDa1OfFXXhkMn23Corh2NbU4AgFolx+jKQlx5/giMqSrCqIoCaDX9rrRBlFydlqNHj+LLL78MS4iNt8vz+PHjsWvXLpx33nmYMWMGVq1ahfz8fIwYMSLuOZ1OJ2bPng2Px4P6+vpkmktERCnicnvR0OJAfYsD9c0OWHv+rm91wNXtBQDotSqMGVqIS6YPwdiqIgwr0zNXhVIq4aDld7/7HX77299i/PjxyMvLC94uk8niBi0PPvhgMPn23nvvxaOPPoqOjo6EVhX94he/SLSJREQ0QDZHN0422oNBSeDv5o6u4DEyAKbCPJQbdRgztAJDS/UYM7QQ5UYdq9dSWiUctPzf//0f1q1bF9wHKBlVVVXBn41GI37+858n9XibzYZjx46hs7Mz5Pbzzjsv6bYQEVE4p8uDNz6sxfZ/18Hj9X/J1KgUKDfpMGZoIS40VaDcqEOFKR9lxVoWfyNRJBy05OXlYdSoUQk/8YYNG4KF5/72t79FPS7eKM3rr7+O1atXQ6fThY3wDGT3aCIi8u+m/K+9Vry+4wg6HG5cMKUc500qR4UpH0V6NUdOKKskHLTcdtttePDBB7F8+fKwhNhIy5E3b94cDFo2btwY8TkTmVp67LHH8Pjjj+Piiy9OtKlERJSAr+ra8NftX+FEgx3VQwpx26IxGFlRIHaziKKSCb0rvcUQmBbqHXULggCZTIYDBw6kp3UAzj//fPzzn/+EQpHdQ5HNzXb4fAm9lFnHbDbg9Gmb2M3IOPZ7cGG/z2hqc+LVfxzBv79shLFAg0WXVGPWhNKcGlXh+y1NcrkMJpM+6v0Jj7QMZCrm5z//Oa688kpMnTo16ccuXboUTz/9NJYtW9avAnPHjh3DypUr0dbWhqKiIqxZsyZs1dJvf/tbbNmyBQqFAkqlErfffjsuvPDCpM9FRJTNuro92PLxcWzdWQe5DLj66yMx99xh0DA/hSQi4aBlyJAh/T6JIAhYtmwZdDod5s+fj/nz5yecH/P888+jqakJf/zjH1FUVBRyXyJ7D91///1YsmQJFixYgI0bN+K+++7Dn//855Bjpk6dihtvvBFarRZffvklvv3tb+Nf//pXSA4NEZFU+QQBH31Rj9d2HEGbvRtfm1iGb10yGsYC/o4jaUl4egjwj7ZE2j8okaXLPp8PH330ETZt2oTt27ejqqoKV155JW644YaYj/vkk0+i3td7Q8dImpubMXfuXOzcuRMKhQJerxfnnnsutm3bBqPRGPExgiBgxowZ2Lx5M8rLy+P268y5OD0kNez34DJY+93c6cbav32OY9YOjKww4LqasageUih2s9JusL7fUu93yqaHnnrqKbz88suYN28etm7dimuvvRabNm3CvHnzEmyIHBdccAEuuOAC/OQnP8FPf/pTPPLII3GDlniBSSxWqxVlZWXBfBiFQoHS0lJYrdaoQcuGDRswbNiwpAIWADFfZCkwmw1iN0EU7PfgIvV+dzrdaGpzosPRDbujGzaHO/i3zdENe++/nf5jnC4vjAUa3H7ddFxydhXk8tzJW4lH6u93f+VyvxMOWl577TU899xzGDt2LF5//XXcfffdmD9/PtauXZvQ4zs7O7F9+3Zs3rwZn3zyCWbOnImHH3444rFPP/00br31VgDA448/HvU5U13G/5NPPsHjjz+O5557LunHcqRFetjvwUVq/RYEAafbu3D4ZBsOn2zHoVPtsJzuRKTfMgq5DPlaFfLzlMjXqlCgU6HCqEW+VoXhlYWYPtqIPLUSzc32jPdDLFJ7v1NF6v1O2UhLR0cHxo4dCwBQqVRwu92YOnUqdu3aFfexK1aswD//+U9MnDgR//Vf/4WHH3446kgHgJBy/QMp3V9RUYGGhgZ4vd7g9FBjYyMqKirCjt29ezfuvPNOrF27Nql6NEREqeDx+nCiwY7DJ9tw6FQ7Dp9sR3tnNwBAq1FgdGUhZo4rRUVJPvQ9wUl+ngr5WiU0KkXUlT9Sv4gR9ZZw0DJs2DAcOnQIY8aMwZgxY/DSSy+hoKAAhYXx50YnT56MlStXorKyMqFzrVq1KvjzQMr4m0wmTJgwAZs2bcKCBQuwadMmTJgwISxg2rNnD26//XY88cQTmDRpUr/PR0SUCLfHh+aOLtS3OHCkJ0A5Zu1At8cHACgpzMOEEcUYM6QQ1UOLMKQkf1BN6xBFk3Ai7o4dO6DT6TBz5kzs2bMH//M//wOHw4H77rsPc+fOjft4t9uNzz//HI2NjZg3b15w00WdThf3sbW1tXjzzTfR2NiI0tJSXHHFFQlttggAR44cwcqVK9HR0YGCggKsWbMGo0aNwtKlS7FixQpMmTIF3/zmN3Hq1CmUlZUFH/fII49g3LhxCZ0D4PSQFLHfg0sm++0TBLTbu3G6zYnTbU40tXf5/25z4nR7F9psruA0j1wmw7AyPaqHFmLM0CJUDylEsUGTsrbw/R5cpN7veNNDSa0e6q+DBw/i1ltvhVqtRkNDA3bv3o0dO3Zg/fr1+M1vfhPzsW+88Qbuu+8+XHzxxaisrITVasU//vEPrF69GldeeWW6m54wBi3Sw34PLunqt8frw1FLB7441oLa+g40tXWhqb0LHq8veIwMQJFBA3ORFubCPJQUaWEuyoO5SIthpQZo1Omrk8L3e3CRer9TltMya9asiMuPzzvvPHz00UcxH/vAAw9gxYoVuPrqqzFz5kwAwMyZM3HvvffGPe9vfvMbPPPMM8HHAcC///1v/O///m9WBS1ENHg0tjmx71gLvjjajC9PtMLp8kImA6rMegwx52PamBKYC/1BSUmRFqaCPKiUyRfHJKJQCQctbrc74m0+ny/C0aEOHz6MBQsWADizDYBOp4PL5Yr72M7OTkybNi3ktrPOOis4vURElAi3xxvceiRZTpcHB0+04YtjzfjiWAsaW50AAFOBBjPHl2HySCMmjiiGLk+V6mYTUS9xg5YlS5ZAJpOhu7sb119/fch99fX1mD59etyTDBkyBF988QWmTJkSvG3Pnj0YNmxY3MfecMMN+PWvf42f/OQn0Gg06OrqwhNPPBG3vgsRDT6CIKDV5oK12QFLUyeszZ2wNHXC0uyA3emGUiGDTqOELs+/PFibp0R+ngq6PCV0mjM/5+cpoVErcLzehi+OtuDwqXZ4fQLUKjnGDyvGN84ZiskjjSg36nJqvx6ibBc3aFm0aBEAYO/evSE7MstkMphMJnzta1+Le5LbbrsNP/zhD7F48WJ0d3fj97//PV566SU8+OCDEY+/+OKLg78IBEFAU1MT/vKXv6CgoAAdHR0QBAFmsxk//OEPE+okEeUWn09AU7sTlmYHrE2dsDR3wtLkgLW5E13d3uBx+XlKVJbk4+yxZgyrKEBLmxOOLjc6uzz+v51uNLY64ejywNHlgS9Cit+wUj0um1mFySONqB5axGkeIhHFDVrGjBkDtVqN9evXY/To0WhubsZDDz2EQ4cOYdq0aTj77LOhUsUeEr300kvxxz/+Ea+++ipmzZoFi8WCp556CpMnT454/C9/+cv+9YaIMsrr86HN1o1Wmwstti60dLjQanOh2+NFYb4ahflqFOSrUZivQYHe/+9ENucLrL5pbu/C6Xb/6pvmdidOt3Whub0LzR1d8PZKfC/MV6OyJB8XTK5ARYkOlaZ8VJTko0CnCn4BipegKAgCurq9cHR50NnlhtPlQblRh0J96lbyENHAxF09tGTJEixfvhznn38+AGDZsmVoaGjA//t//w+bNm3CuHHj8MADD4Q9LlYl295SXdVWLFw9JD3sd2xd3R50dHajvbMnKOnwByatNlfPv7vQ3tmNvr9BNCoF1Co57A53xOqteWrFmYBGr0GhTo18rRLtnd1oau/qCVBCV98AQEG+GiWFeSgpzIOpMA9lxYHgRIf8BHJJ+H4PLuy3NA149dCRI0cwY8YMAP6quDt27MCmTZswcuRIzJ49G4sXL44YtPSuZOtyubBt2zZMnjwZQ4YMgcViwd69e3HZZZdFPOef//xnLF68GGq1Omq7uru78fLLL+O73/1uvC4QSYIgCGizd0OllEOXp4Q8xbkSgiCg2+1DY4sDxywdaO90BYOS9s5udNi70e7o+buzGy63N+w5NCoFjAUaGA0aTB5pQrFBA2OBBsWGPBh7ftZqlJDJZPD6fLA73MHnb7d3o73T5T9Xz59Tp+3Yb++Gw+WBQadCSWEeqkr1mN6z+sZUqA0GKYmM0BBRbosbtHi93uD0z2effQaz2YyRI0cC8JfJ7+joiPi43pVsb7/9djz66KMhRei2bduGrVu3RnxsU1MT5syZg4svvhgzZ87EyJEjkZ+fj87OTtTW1uKTTz7B+++/H1yRRCRFrTYXjlk7cMzagVprB2rrbejs8gDw1/XQ5Smh16qg16qQ3/N38OeeMu56rf//ZmeXB51ON+xONzq73Oh0enr+9udvBG73eCOPBubnKVGo16BAp8LIyoKQqZ2CfLU/ODGcCUgSoZDLUajXJDS94vMJrPhKRHHFDVqqq6vx5ptvYt68ediyZQvOO++84H0NDQ0wGOLvJvn+++/jV7/6Vcht3/jGN/DTn/404vH//d//je9///tYv349/va3v+Grr76CzWZDQUEBxo0bh4svvhi33347iouL456bKFHdbi/sgQt/r4t94I+jywO1So4CnRqGfDUKdCoYdD0Xdp0q5gXd7nSjtidAOWa14Vh9B9rt/n1l5DIZhprzcc64UlSV6uHzCf5z9gQddqcbbXYXTp22w+70RBwB6U2tkvv3pMlTQa9VotyoQ75W2fNvFcrMBsgFXzAwMejUoieXMmAhokTEDVruuOMO3HrrrXjggQcgl8vx17/+NXjfli1bcPbZZ8c9yfDhw/Hiiy+GTOX89a9/jbnk2Wg04qabbsJNN90U9/lp8BIEAZ1dHrTbXejs8l/Qu93enr99cEX82f9vH4CW9q7giERg35dI1Eo58rUqdLu9wdGQvhRyGQry1TDoVCjoCWY8Xh+OWTtwuq0reFy5UYeJw4sxoqIAIysKMKxUD3USUx9ujw+dXWeCKwDBzfP0WiVUytjPJfU5byIavBIq42+321FbW4sRI0ZArz+TIHP06FHk5+eH7NkTyf79+7F8+XJ4PB6UlZWhoaEBSqUSTz75ZM5sUMhE3NQSBAFOlxdtdlevP92hf9v8P/dN2IxEIZdBo1JAo1ZArZRDo1JAn6+GWiHvNe3SM+WSFzolk5+nDAkqPF4fbA43bI5udDi6Yet0o6PPzzZHNzo63ZDJgOHlBoysKMDIcgOGlxdAl5dwTce0yMb3OxPY78GF/ZamlJTx1+v1EZcnjxo1KqFGTJw4EW+99VZww0Sz2Yxp06bFXSpNg4NPEHC61Ylj9R2otdpQa+3AiUZ7SL2NgDy1AkV6DYr0alQPKQz+XKjXQK9VBVeu+P9WBP+tVIRPf/T3P7dSIUexQZPSTe2IiCi+jH3lU6lUwVVINHgJgoDm9i7U1tvOBCn1Njhd/ikXlVKOYWV6nD+5HCWFWhQZ1CjuSeYszFdDqxF3lIKIiMTDKwClXUdnN7Z/ehK1PUGKvScPQyGXYWipHudOLMOIcgNGlBtQWZIfcVSEiIiIQQul3WeHm/Dmx8dRYfLvfjuyogAjyg0YataLvmqFiIikg0ELpd1FZ1XiginlUMgZoBARUf/xKkIZwYCFiIgGiiMtKSL14lhSb39/sd+DC/s9uLDf0hOv7QnVaSEiIiISG8fsiYiISBIYtBAREZEkMGghIiIiSWDQQkRERJLAoIWIiIgkgUELERERSQKDFiIiIpIEBi1EREQkCQxaiIiISBIYtBAREZEkMGghIiIiSWDQQkRERJLAXZ5TpLW1Ez6fNPeeNJn0aG62i92MjGO/Bxf2e3Bhv6VJLpehuDg/6v0MWlLE5xMkG7QAkHTbB4L9HlzY78GF/c49nB4iIiIiSWDQQkRERJLAoIWIiIgkgUELERERSQKDFiIiIpIEBi1EREQkCQxaiIiISBJYp4WIegiwOT2wO93Qa1UwaJUAZGI3iogoiEELEQEQcNjSgX1HmyEIgEwGTBplQnVlARi4EFG24PQQUVYSYHO6YW1xwOZ0A0hvhUub0xMMWABAEIB9R5thc3rSel4iomRwpIUo62R+1MPudAcDlmArBP/tBq0qLeckIkoWR1qIsowYox56rQqyPvGQTOa/nYgoWzBoIcoysUY9EpP81JJBq8SkUaZg4BIY3fEn4xIRZQf+RiLKMoFRj96BS+KjHv2dWpKhurIAZcU6rh4ioqzFkRaiLDOQUY+BTS3JYNCqUGHU9eSxMGAhouzCkRairNP/UY/0JNRmY/2WbGwTEaVbTgcta9aswVtvvYVTp07hjTfewNixY8OO8Xq9ePDBB/HPf/4TMpkMP/jBD7Bo0SIRWksDk2sXMf+oR7KBxsCmliLJxvot2dgmIsqEnJ4e+sY3voEXX3wRQ4YMiXrMG2+8gRMnTmDbtm145ZVX8OSTT+LkyZMZbCUNnP8i9u6nddi5rx7vflqHw5YOJF7bpD81UTJbRyVRqU6oTe1KptS8ZqwpQzR45fRIy4wZM+Ies2XLFixatAhyuRxGoxE1NTXYunUrbr755gy0UGoyMZqR/DmiXcTKinUJjFT051t7Or/pD/Q1Tm1Cbeqmm8JfsymjTTAXaWF3erJgCoyIpCCng5ZEWK1WVFZWBv9dUVGB+vp6EVuUrTIxJN+/cwzkItafgGdgQVIsqXqN+ze1FEnv6SalQoZ8nRpujw8KhRz+kZLE2tX3NVPIZThY14b/HDwNpUKeVF9TPwVGRFIx6IOWVDGZ9GI3YUDMZkPM+5vaHKhtsEOn0wRvq22wY8xwI0qKdAM+vyAIOGZpx2eHmqBSKaDTKCGTyRI6h0ylgP54a9hFrLLMEL9tCnlIn3rfHu01sZ1qS/oxiUj3awz4X+emNgds3V4U5KthKtRC1reqXC8lgoCZLi++OtECt0fA50eaYSrIw+dHmjBpVAmmVpfEfHxA39dMn6fCzv31qCzJR36+//ZE+xpo0/5jZ4K7iSNNGFlVHLctA3l/pIz9Hlxyud+DPmipqKiAxWLB1KlTAYSPvCSqudkOny878hqSZTYbcPq0LcI9Z6YqXG4f7HZX2BGWBhsEt3eALfCPMBy1dODwyTbIAAwx6zGkVA+324cT1nYIbg/Cv4H729fZ5UalSYdDJ1pDRigEtydKv/zMZgPg9cHhcIUFPPD6oj+2P49JgLXFkcbXGAi8zrUNdtjtroRHNyqLNFDKjNj+yQkML81HkSEPbrcPX9U2o0Cj6DXCEWNqq89rJnh9cLncgCCgs/NMnxPta2WRBobxpSHnamqyx3xM9M95bmO/Bxep91sul8UcBBj0Qcvll1+OdevW4bLLLkNbWxu2b9+OF198UexmxREr7yFVeSehUxVFBg3a7N0o0quDR0Qeku9/TkqBXgO5XAaVwn/8x/vqIQfQ0emCa6y5z8U1tH0qpQyTRpmQn6dKqt+BxNV9R5uhkMug16lhKsqDf+oj8vRH78f0DpIGWj023dMegdc5MOKR+LSWDF6vDwX5KsgVcuw60ACfT4BcLkORIQ/TRhsBIObUVt/XTK2So8yYD7XyzFqA5PqauikwIpKOnA5aHnzwQWzbtg1NTU244YYbUFRUhM2bN2Pp0qVYsWIFpkyZggULFuDzzz/HZZddBgD40Y9+hKqqKpFbHkusvIfYF47A48ODinB9cxDsjm6UmbTo7vagQJ8Ht8eH6iEFAARYWxw9z6XAYYst6fMHclI6Hd2YPMqEdns3Pjt0GnqtCkPMeigV8rCLa9/2uT0C9h1txuxzqpK8kPkTV8uLdThs6cDhula02Vw4erI9xihEeqrHpisYCrzmluZOuNw+aHtFRYnm/ui1Kuh1anzSE7AAgOATcLiuFaN7Pnux83xCXzODVoWhpfo09JWIcllO/4a49957ce+994bd/oc//CH4s0KhwKpVqzLZrAGJlQQKxLtw+AOeg8dboNP6EypHVRZEHIrrm9zq8QpQKgQMqyjEgaMt0OYpcLCuDe9/ZkWRXh286PRNtjzZaIdSoYCpQBM1qCkr1kIm6zkHfBhSqoelqRPlJh3yNcpgX3pfXFOxgkQQ/Etw7U43FAo5jlvboVTIo7x2faXjm346gqEzQW6BXoPj9R1weXww5Plf10RHNwxaJUxFeRB6AhYZAHOxDkqFPLgnUvz3I/Q1q9Zy2wAiSk5OBy25IXRkItLFWiGXoa3TBUeXBy63DzqNwr/Kw+2DSiVHZ5f/wmFzenDweAtk8jND/J8fOg2ZXI7R5Xr0vmBEmqrI06hwpK4NujwlCg0a7DrQAMEnQJenhFopx1FLB1xuH9RKOZQKGeQKOT450ICTjXYYdKqwoCYQGJSfUxW8z+MV4PP6YCrICwYsQPjFdeBTKQL2HG7Cri8sEARAp1WhucMFo+FMsmjqltEmM2UWLRjq37Rf7yC309GNSaNM+OpkOzRKHTQqeRKjGzKMKDNg9JBCdHV7oVYpoFbKQ17zSO+H/3PnjtLuRAK/XCsaSEQDwaAlq0WeCup9cVAqZFAo5dj5RT1MRVrUN9sxtLQA+3uCEoVchjKjDuXFWtidbui06mDAAgBen4DdBxtRWpgHg1YZvEAYtKqwqQpTUR7abP6kSbfbF3yObrcXaqUcKqUcHo8/aMnXqYNBjVqlgCAgJKgJ9lAAbE530lMHA51KsTk9wdUnAKBSytHc7oReqwq2T6WUQaGQ95r+6s8FMxX1SZJZCh09yA2MZJ0/qQKFBhU0SiVMBeq+J4vKoFVh2lhz1Ne87/sxZbQJ9a2OASzhZuVbIgrFoCWLRZoKOni8BWOGFQdXyuh1atRabSjSq9Hp6Mb0cWXY8uEx6HVqKOUyVJjy0djigE6jgi5PCbfHF7LKSQZApVKgs8uNhj4XmCmjTZh9ztDgxRUQcPRkuz/xVSWHXC4LBiUA4HB2Y9o4Mw6daIXb7YPgE2Au1vUKAs4ENcHzB7+pJz91UF6sg2a8Al4vYCpQhwRd8RKU+45YBUYh2jpcPQGYDKUmPT7aaxnQBTMV9UkSrwsTP8gFgA5nN07UtyddHyXe9FXf+wAB7356st/1bNJXD4eIpIpBS9YJXWbce0QlMOVTkK8KBhMuty84+uHxCnB1e1BmzIdBp4KxQAONWhmcoik2qDGkvAAKuQxenxDMSyjIV8HrAz7Z1wClUg61Ug5BAPYe8Se2Vhh1wbYFvk13OroxZbQJDc3O4DTBuOFGVFcaUGXWo63ThY5OVzBHBAgNagIrfsYNNwZzIhKfOog8etHQiijfyiMnKPcuI+/xClDJfKiZNQxer794WiBgAfp/wewbHAVGoCpN+dBr5Qk9b6L5O4kGuaeaOkNyhZLrV9/3RQib/gncZ21xwOX2+UfieqaTkplyY+VbIuqLQUtWibzMuKRQE1xqKvgEdHS6MK1nCbDN6Qn5Jq1QyOH2eGHQ+etp9J6icXsENJy2Ye7XRuCLw01QKuXIz1Og2KDFvmPNONFoCwYyRoMmYiJl32kcAULYNIdBK4dBq4Srz1RC76Cms8uNFpurX0P/kS7OJxrsaGpzRkykBcITlI+cbEVVRTE+a/YHahqVHOOGG1FaqAEgg7XFkZILZt/cm8AIVGB0KvC8nV3+wC3SCEai+TuRLvJujwCjQYPZ51QFA+FurwCHo3tA/ep5ZMyVbJ1dbhyv7wgJkE0FmoTzjpKrxsvcF6LBgEFLFul9MVYqZFAoZBhSqodP8OHzQ00QfAKGmPUwFWlx1NKBgnwNSgtVGDOsGJ8dPA2lUg6HsxuXnFMFS6MteIEcYtbDXKwNJuaWFedh5NdHBlfNfH6kCSqlf7rH5xNwutWfw6FRySNcYMJHQAzaSHkR0acSDFp/YLFzXz0U8jMjSCcb7Sgv1sW9qEW6OHe7fejq9kKvDc2XibSyRamQwSvIcOh4MyrM+cFVVNWVBvgvdAIUCjkcXZ7gyBPQv5opidQnUSllaLG5sHNffUI1TqKNUEULbvLzVMH3zOZ0Qy4PvZj3txaMzenGZ1+dDknM7R0oHjzegkmjTPjiaDN8PgHN7U58bXJ5lLyj8KAj0O9A8vi/DzTAVKiFs8vdJ8Dt3/5RDHKIpIdBSxYJXIwDK28++qIeKoUMZ40pRZFeA3ORBhq1KphI225zYcSQQjQ22/tcfPWwVRWhrdMFp6sbKpUy+JhAYm7ZMC0MWhWsLQ4AsmCNlMAFxuPx4exx5gHWzYg+xWN3uqGQy2IUK4t0AfFfaDw+HzxeX8jUk1olR55aEXJ0IJHW5faEHJ+vU+PfBxowdrgR7T1Ta2emSGTBZeFFBRrsO9oMU6EWpgJNP+uIxK9PMm64MeEaJw6XGw2tXcGpvMAKoOrKgoSSkw1aJSaONAVXTfW/PoqA2gYbjpxqD455BEboAsGU2yNAqfBh5oSyYMDsX50VOkJid3qCNXL65tlUVxagIF/jr8ZbXhCcYur9+kTLfSkv1kHAmdGrkmA0xwRfIqli0JJFAt+UA3kPPp+Abp8Ar09Au92FkZWF2P1VI3w9w+1FBXn4x6d1GF5eALen78XX/+3RNaoE63ccCT7GVKjFoROtqDLrYdCqgucMrCyZOaEMbo8P08aYg1MlqXPm261CIY9ZrCzSkt/AhcY/OqNCQ7MzWCNmWJk+JBjonUjb93i3xwdToRZajTI4TdJ7VObMaJcPM1LyesROMk4sd8M/4tLQ6sBbH9eGTLn0fs/DR7cUYSMKU6tLYNAoBjTKYHN60NzWBVlPMrYA4HSrAwU6VcgSaI9XCAaGMpd/1KdXL3HY0oGTjXZ80jONGQh8evfJ6/VBlxf6q6r36xOtDMBhSweOW9uDgclMlxeVRZqEgxyOvhBlHwYtWSTwTfmopSMYZJiLdXC5/MPhrm5vyO1CT0ATWHIM9L3YyZCfp8Lw8oKoyZC9v3l7vAI67C5MGmXqc4FOdCg99vYCfcvulxjzoxYr6xu09L7QeLwCAB9GVBgwoqKwp3Cd/6McuGD3TqTte7wuTwlnlztkc73AFEnfJcKBC67X6+tpR7SaI8m8FuEjUInkrNicHhy1+HNE/GdAcCqv93t+5rkjjyiUlBgGXBjP7nTD3md0TiaXobqqOOoS6L4jOoH3VKtRBQPXQH/UyjOfg3g5PZHu1+vUwZEbwH/f/mPNwf2KEglyOPpClH0YtGQVWXA4vKnVGcynCKxsmT62DB12V/B2lUoOhVwWktQZqQibRiWPucfLkBIdvONLey0d9l/8/BIdSo99XKSy+y6XB8PKDfB6hYjFynqLVKG3zeaCZpi8T36NKjjt1XvlCiAPHl9a6J/qqW2wB1+P3hfUaEXSYr8OZ4IUg1aVVH2SRGvO2J3ukNwj/6vuf8ZI9WSijSiMGW4Ma0Oy9FpVT/B0ZvpHrZKH9DFedd/AexpYPu/rGbHpdntD8ql657b0ruRs0Cqivn69awoFBIL1RIMcLq8myj4MWrKODKWFGsyaVBaW9zDElBdye++k2/4VYYu862/veieKnn1/4i39jVdTI9K32w67CxNGmMK+3UbKr0iuAq4QceVKWXFez8XdifJiHaqHGWFttPVJEo78egkQYvRPGbbqK1A7J9Zr1vs9T6R8v16rgsMZOrqh0yhQVWGIWE8m2rRTR2c3DMH8H39OSWunK0rQGlnv16nd5v/sjBpigj7kvYtd8TbwnvbOpxJ8AvLUij6fAxmqKw3o9viCCef7jjYDQDBIilQjJlBTKNians9LskEOgxai7MGgJStFv4hFzFmoKopxsYv+XDanO2zX34PHW9Dt8QXreiRa3j5eXkakoMPrE1BdWYDRPRfYWFMuBq0iZJVUrBL0ge0Keq9csTtcmDjKGHJxnzm5EpVGbUKvl7XFGbV/QOiS6m63Dw0tncHtDaK9Zj3PEjKNVBHWnt6vgRLjhhtx8HhLMPdo9JAC7D7YiK5uX9gKnmiBXkG+GoLbC0DAUWsHDta1Ye8Rf8BQZszH18+qSGBapL/7JIWOSAWCB8CHWRPKYCrKw4gyQ1jgZHN6cehEazC3JVKyct/6MX0Dk4kjTSH/j8qLdcFgTZeniBrkEFH2YNCStaJ9S4205Fge59tg5OeKFGjotGp8dvB08OIQqbx9pF/m8UZCoo1g6IMjHLH3nzlsseHYqbYoS5RD2Z3usJUrhQYNjpxsg65XUbVAjkMir3Gs/vV9HVUqOWRyWUiuUeQtAZLflbu60hCyEulYQweOnOqIuIKnwqiN+JqbCrVoarLD5vTgRIMde480B6ebGlo68dlXpxOcFkl208jIRQF7V12OFvgkX2guPKgaWVWMpiZ78IjeU3gqpQyVpYaQUcspo/0FCAe2jQMRpRKDlkEscCHuze3xQdkr/6VvefvwKRz/RbWzyx1SeTX8uP7vYNx76il8ibI87PjeK6ICx0OGkCXSQHLD//Gm2TxeX7BeicvlxozxZTjZaEe3x4f8PEXELQHKirUJ7codKagJ1FyJvYIn8mseSEC2O93ododu6yAA6Or2pmVaJNIUYnjV5cj6t0FmeFDVe1fvvjlWjc12nDelEl6vL5iXFNiGgIm5RNmBQcsgFrgQ905IHVVZEPLLvG95+9BgI3xF0KRRJuTnqaJOVfVn1Uqy37IjBRh9+xXob+LD/9GCLuB0mxP5OhWOWjugVsigqihEc0cnqsr0wVGhfUebIAiyYNv3HW2GckxpzH4lkicUbwVPrNdcr1VBrQpN7JUBMOiUUCjkqG91QC6XR3jf+2cgZfkjvafJjYTE39Xb7RHg9fpQYdQFp07j5XIRUWYxaBnU/BfiMcONsDQEElL9CZp9k4Aj1SiJtCJo31H/N+fU/WLvT3XayLk/fft1JschUZG/ue894q8dM3NCGTQqBf79ZSPKjbrgKI9/d2sBauWZ108QAIUi9lLnRPKE4q3gicWgVWJYmR7Obk8wp2VoqQGVpQXYtd8KmVweVlxvICMN/RstCR4ZVqQvmZGQRHb1Tua1JyJxMGgZ9GQoKdL1JGb6JTqNk9gv9oGUSxcGUJ02PMCIl+PQH4HXIDAVpctTwdHl7pPPEnl36+J8TcylzsnkCUVfwROLDKMqClBapMPkUaZgQupHe60o0GuCBQ4DtVMGOtKQ6NLuWO3tvR1BpM0hC/I1EUeG4u3qnexrT0TiYNBCESQ2jRP/F/vAyqWH7sWUiuq0of3qXVyuv/q+BpFq5/Td3bp3EnLf6ri9L7TxL/L9zxPq/ZrotWeq2AY2inT3ynUJ1E7pXfCtfxJpb2JBbt8gRKmQQSaXY/snJ6DLU4Z91vrmb/We9vT5fMFpMJvTg977HvU/wCKidOD/QOq3eL/Y4+VkxBO7Om0mkyH7XkgVsDnPJKv2fg0i1c7pvbt15OAkWoCYyEW+f3lC0QQu7r0LvskAqFWKFI00xGpv4kFu32AxsJ/U8HL/DtN9P2uR9lzyT3uqcdhii3jOgQeERJRqDFpoAGJfVAeaF5AdQ/ThycalJn3Y0tjQZbuRa+fEX5oeSWqDknh6V5+d3BOMmQq1MevipEoyQW7fgDmwn1TvKbjQz5os4p5L8c6ZydeeiOJj0EIDFHt1ykCCjmwYou97UdNp1cFNKgP7OEVattu/ACUbnAlEO7v8S7dTtXoonuSC3NCAWaGQw9nljvlZk8nCP6v9D6wHkqtFRP3FoIXSJhWJl2IP0fe9qLndvjibVOaCgYzu9P9innyQG7o5ZH8+a4mdM3x6MNqUEgMXovRi0EJplJpEUTGH6BNJtOWqkoCBJV4PLMjt32ct/jkj94k1XIjEwaCF0kzcoGOg+l7UEtmkcrAaaOJ136mpvit64gc+/fmsxQ52IvXJX3fHFyN/hojShb9piWLqzyaVg1NqCrL5d9pu6LUvUPqnX6IHO5H6FK3uDkfbiNIvfOMWIurDf1GrMAZGDOR9/s2ABYi8l1V/LubRRmxsTk+KWpq4QJ+UChkKDRro8lRQKWSYPs4c7CtH24gyh//LiCglUrXaK5tK6Bu0SkwZbcLBujbsOtAAwSegzJiPypL8hHanJqLUYtBCRCmSmtVe2VGfJ3hmmIu0+M/B06g05UOtUkCtlCe8OzURpVbOBy3Hjh3DypUr0dbWhqKiIqxZswYjRowIOebJJ5/EX//6V5SWlgIAzj77bNx///0itJZI6gaeeJ0N9Xl6szs9UCrk0GuZeEsktpwPWu6//34sWbIECxYswMaNG3Hffffhz3/+c9hxV199Ne666y4RWkiDE4uTRSd+fZ7esmvkh2hwy+lE3ObmZuzfvx/z588HAMyfPx/79+9HS0uLyC2jwc1f++PdT+uwc1893v20DoctHfBvTUh+fZOfxQvoAiM/TLwlEl9O/6+zWq0oKyuDQuEvBKZQKFBaWgqr1Qqj0Rhy7ObNm/Gvf/0LZrMZP/7xjzF9+nQxmkyDwMDrmVBmZdfID9FgltNBS6IWL16MW265BSqVCh988AGWLVuGLVu2oLi4OOHnMJn0aWxh+pnNBrGbIAox+m071QadThN+h0Kesfbw/e7HY1PYjkzj+z245HK/czpoqaioQENDA7xeLxQKBbxeLxobG1FRURFynNl85tfRBRdcgIqKChw6dAizZs1K+FzNzXb4fNIc3jebDTh92iZ2MzJOtH57fXA4XGE5EvD6MtIevt+DC/s9uEi933K5LOYgQE7ntJhMJkyYMAGbNm0CAGzatAkTJkwImxpqaGgI/nzgwAGcOnUKI0eOzGhbafBgjkQmCLA53bC2OGBzusF8IaLckPO/JR944AGsXLkSa9euRUFBAdasWQMAWLp0KVasWIEpU6bg17/+Nfbt2we5XA6VSoVHHnkkZPSFKLWYI5FekTc5LCnJ3SFzosFCJgh9a09Sf3B6SHrY79xkc7rx7qd1YdNvV186BoLbK17DRJLr73c07Lc0DerpISIafKJtA9DR2Z3gM3BqiShb5fz0EBENLtGKwRXkqxMYaYk8tZS+HaaJKBkcaSGinBIp0XnKaBMEAXFHT1Kzw7QAu9ONuiY7ahvssDm7o56PiJLDkRYiyjGhic4GrQr1rQ5s33UCdrsr5uhJYjtMx9qCQcBRawcO1rVh75Hm4K7QXz+rgqM1RCnAoIWIctCZjRttTjf2HW0OFvSLVYE4/j5DsaePbE4PTjTYsfdIczAxv6GlE599dZoVj4lSgNNDRJTTYo2e9BWvhk686SO7041uty9kJaEAoKvbG/F8RJQcjrQQUU4LjJ70Fn2X5tg1dOJNH+m1KqhVcsjlsmDgIgOQp1ZwV2iiFOBICxHltOQrEEffYTpeAGTQKjGsTI8po02Qy2WQASgz5mPaWDMrHhOlAP8XEVGO84+ejBluhKXBNqAKxIEAqG9Oy5mARIZRFQUoLdJh8igTvF7AVKAOC36IqH8YtBDRICBDSZEuBRVxE9mCQQZ9z1QREaUWgxYioqScWZlERJnFnBYiIiKSBAYtREREJAkMWoiIiEgSmNNCRJRRsbYBIKJYGLQQEWUMd5EmGghODxERZUhqdpEmGrwYtBARZUgy+yARUTgGLUREGZLcPkhE1BeDFiKiDEl+HyQi6o3/U4iIMiaRbQCIKBoGLUREGcVtAIj6i9NDREREJAkMWoiIiEgSOD1ERJRxrIpL1B8MWoiIBiyZIORMVVyFXAa9Tg1TUR5GlBl68lwYvBBFw6CFiGhAkivNH6iKq5DLIFfI8cmBBgg+AaOHFGLaWDNL+hPFwJwWIqIBSLY0f6Aqbr5OjS+ONsPnEyAA6Or2sqQ/URw5H7QcO3YM1157LebOnYtrr70WtbW1Ycd4vV6sWrUKNTU1mDNnDtatW5f5hhKRJNmdbrjcPtidbnR7fABil+YPVMV1u33w+fyRjgyAWqVgSX+iOHI+aLn//vuxZMkSvPXWW1iyZAnuu+++sGPeeOMNnDhxAtu2bcMrr7yCJ598EidPnhShtUQkLQI6u9w4Xt+Bk6ftOGZpR4vNFbM0f6Aqrlolh1wugwyAuVgHtVLOkv5EceR00NLc3Iz9+/dj/vz5AID58+dj//79aGlpCTluy5YtWLRoEeRyOYxGI2pqarB161YxmkxEEmJzenDweAsmjTJBLpdBANDc7sSYYcW9SvMLsDndsLY4YOsZRamuLMCMcaW4bNZwjB5SCKNBw5L+RAnI6f8dVqsVZWVlUCgUAACFQoHS0lJYrVYYjcaQ4yorK4P/rqioQH19fcbbS0TSYne64fYIUCp8mDmhDG63DyqVHEaDBv5Jn+hJunqtCtNGGzG6soBLn4kSlNNBSyaZTHqxmzAgZrNB7CaIgv0eXFLdb5lKAf3xVggC4PEBMoUcXgGoKDWgpEiHpjYHahvs0Ok0wcfUNtgxZrgRJUU6f5tS2qLI+H4PLrnc75wOWioqKtDQ0ACv1wuFQgGv14vGxkZUVFSEHWexWDB16lQA4SMviWhutgeT6qTGbDbg9Gmb2M3IOPZ7cElPvwWMKNOHjaQIbg9On7bB2uKA3e4Ke5SlwQbB7U1xWyLj+z24SL3fcrks5iBATue0mEwmTJgwAZs2bQIAbNq0CRMmTAiZGgKAyy+/HOvWrYPP50NLSwu2b9+OuXPnitFkIpIU/67Ns8+pwrmTyjH7nKqQOiuBlUIhj4iYbNs370WaX4CI0i2nR1oA4IEHHsDKlSuxdu1aFBQUYM2aNQCApUuXYsWKFZgyZQoWLFiAzz//HJdddhkA4Ec/+hGqqqrEbDYRSUb0XZsDK4X6jsSEJtsmV5yOaDCTCYLAkD4FOD0kPez34CJev2OX+Lc53Xj30zr0/k0skwGzz6mKGAgli+/34CL1fsebHsr5kRYiInFFH4kBzlTI7S1QZC4VQQtRLsnpnBYiomyXeN4LETFoISISUSDvJRC4sMgcUXT8X0FEJCr/CqSyYh2LzBHFwaCFiEh0sfNeiMiP00NEREQkCQxaiIiISBI4PUREJCmx674Q5TIGLUREksHquTS4cXqIiEgibE5PMGAB/EXo9h1ths3pEbdhRBnCoIWISCJiVc8lGgwYtBARSQSr59Jgx6CFiEgi4lfPFWBzumFtccDmdAOQ5iauRNEwEZeIKO1SteInVvXcyEm6JSWG1HaFSEQMWoiI0irVK34iV8+NlqQ7ZrhxwD0gyhacHiIiSqNMrfiJlqTb0dmd0vMQiYlBCxFRGmVqxU+0JN2CfHVKz0MkJgYtRERplKkVP9GSdE2F2pSeh0hMzGkhIkqjQDDRN6flzIqfVImcpCvrGzERSRiDFiKitIq14if154qUpEuUK0QPWtrb2/Hee++hoaEBZWVluOSSS1BUVCR2s4iIUihVwQQ3S6TBTdSclt27d2POnDl4+eWXcfDgQbz88su47LLLsHv3bjGbRUQkkljF4fxLp9/9tA4799Xj3U/rcNjSgfQVkGOhOso+oo60PPTQQ7j//vvxX//1X8HbtmzZggcffBCvvfaaiC0jIsq02PVcoi2dLivWpWE6iLtJU3YSdaSltrYWV1xxRchtc+fOxYkTJ0RqERGROOLVc8nkZoncTZqylahBy/Dhw7F58+aQ27Zu3YqqqiqRWkREJI54QUniS6dDp3WEvk+agrYQiUXU6aG7774bt9xyC/7yl7+gsrISp06dwvHjx/G73/1OzGYREWVcICjpHSz0DkqiL51WwOZ0w+50w6BVob7VEXLMTJcXlUUaJDOtE68tRGIRNWg5++yz8fbbb+Mf//gHGhsbcemll+Liiy/m6iEiGnTi13OJtHRagcMWW/AxRQYNaq02FOn9VXAFAdh/rBmG8aVJ5b1krrbMQHAl1WAk+iewsLAQCxYsELsZREQii72Dc+8LdIVRC39yrjsk96Tb7UNDSyd0eUqolf7Z/8C0TnLJuonUlhEzaBhoojADHqnKeNBy00034dlnnwUALFmyJGq1xhdffDGTzSIiygKBei5K2JweWFucEad8AhfovrknKpUcMrkM3W5vMGjp/7ROrNoy4q4uGthKKq6MkrKMBy1XX3118OdFixal7TxOpxM//elPsW/fPigUCtx111249NJLw47buXMnfvCDH2DEiBEAALVajXXr1qWtXUREsYVeVCNN+QQu0H1zTzod3Zgy2oROhz9hViYDJo5M/bROZpdfh4uVKBzv/GK3PXkcFeot40HLlVdeGfx51KhROOuss8KO2bNnz4DP8+yzzyI/Px9vv/02amtrcf3112Pbtm3Iz88PO3b06NF4/fXXB3xOIqKB6ntRjTXlU2HUhuSeeH0CJlYVwVykhd3pgV6rwsiqYjQ12VPaxoEEDakwkERhsdueHI4K9SXqkucbbrgh4u0333zzgJ/7zTffxOLFiwEAI0aMwOTJk/H+++8P+HmJiNIp1pRPQO8LdHmxDmePL8W0saWYfc5QjKoogEGrRoXRP3KQjg0TM7VzdTTRdrROZERJ7LYng/VywomSiOvz+SAIQsifgBMnTkChUAz4HBaLBUOGDAn+u6KiAvX19RGPra2txcKFC6FUKrFkyRIsXLgw6fOZTPp+tzUbmM0GsZsgCvZ7cJFCv2UqBfTHW88ELjIZzh5fBkeXG1qNKjjlM2JoEfYeacb+Y2e+has1JoysMoQFKqnud4kgYKbLG3LuiSNNGFlVnLFdpUtKDBgz3IiOzm4U5KthKtQm1O9saHuibKfaoNNpwu9QyGO+p1L4nPeXKEHLxIkTgx+OiRMnhtwnl8txyy23xH2OhQsXwmKxRLzvww8/TLgtkyZNwo4dO2AwGFBXV4cbbrgBZWVlOP/88xN+DgBobrbD55Pm3hxmswGnT9vEbkbGsd+Di3T6LWBEmT5kSmDKaFPIlI9Bq0TtyTbs+sISMiqz6wsLDBpFyDRHuvpdWaSBYXxpSK5FqqehEmFQKyC4vWHnjtXvbGl7XF4fHA5X2DQYvL6ofZPO5zwyuVwWcxBAlKDlnXfegSAI+M53voMXXngheLtMJoPRaEReXl7c51i/fn3M+wPF6oxGIwDAarXi3HPPDTtOrz/z4lRVVaGmpgb/+c9/kg5aiIhSI/pyY4NWHTxK/NyMVO1cLQZptF0a9XIyS5SeB6Zt3nvvvbSd4/LLL8crr7yCKVOmoLa2Fnv37sWjjz4adlxjYyPMZjNkMhna2trwwQcf4Lbbbktbu4iI4ot/UWXV2lTJ5tU5idTLGVxED9feeecd7Nq1C62trSG5LY888siAnvemm27CypUrMWfOHMjlcqxevTo4qvL444+jtLQU1113HbZt24aXXnoJSqUSXq8XCxYsQE1NzYDOTUSUbol+CxcEIVjmP3cueqkKNKSwOkcao0KZIhP6s5tWijz11FN4+eWXMW/ePLzyyiu49tprsWnTJsybNw/33nuvWM3qF+a0SA/7PbjkZr/jXbwFWNpcwdwXlVKGccONyM9TSTiASSzQSOT9tjndePfTurDRqtnnVEk2SJD65zxeTouoS55fe+01PPfcc7j77ruhUqlw991343e/+x1OnjwpZrOIiCTC/y08sLy5bwBic3qCq2SUChlkcjnW7ziCf35uwbuf1uGwpQOAtL5spXIZMHezlh5Rg5aOjg6MHTsWAKBSqeB2uzF16lTs2rVLzGYREeWE3hflfJ0aXxxthtcnoNvtlWzNj1QGGlKq2UJ+ogYtw4YNw6FDhwAAY8aMwUsvvYQNGzagsLBQzGYREeWE3hdlt9sHn0+ADIBa5a+FJcVRhVQGGgMpUicN/nwma4sDNqcbUhtVi0TUd+YnP/kJ2traAAB33HEH/ud//gcOhwP333+/mM0iIsoJBq0SE0easOsLC1QqORRyGUyF2hRspiie1C4DzuXVOVJIMk6eaEGLz+eDWq0O7j00depUvP3222I1h4goB8kwtboEBo0CnV1ulBl1OHSiVQI1P2IlGKc60MjN1TnS2xgyMaJ9WuVyOZYtW4bdu3eL1QQiopwnk525KJcXa1Fl1mdwVCH+6qbw+5HACEFuBhqpJH7xwfQQNcSeOXMmPvvsM0ybNk3MZhARDRKpvtjHCkriTU9Evr+sWJuTIwSZlqvFB0UNWiorK7F06VJ84xvfQHl5echmVaxKS0SUzWIHJfGmJ6LdrxxTmpMjBJmWq1sAiNp6l8sVrD7b0NAgZlOIiCgJ8YKSeNMT0e5XKJCTIwSZl5tJxqIGLb/4xS/EPD0REfVTvKAk3vREtPuL8zU5OUIgjtzL/RH1U1BXVxfxdrVaDbPZDLlc1DIyREQURbygJN70RLT79VolqrW5N0KQKbm519QZogYtc+bMCeaxCIIQktMil8sxe/Zs3H///SgpKRGriUREFEH8nIl40xOx78+1EYLMELDncFNwr6lcqc3Sm6hBy89+9jPs2rULy5cvR3l5OaxWK9auXYvp06dj5syZ+NWvfoXVq1fjiSeeELOZREQUJl5QkshOzLk3fSGm3ntNAbm58krUoOXJJ5/E22+/DY1GAwAYPnw4HnjgAcydOxfvv/8+Hn74YVx22WViNpGIiKKKFnTEX+4cP6ChZOVqbZbeRA1afD4fTp48idGjRwdvs1gs8Pl8AACdTgev1ytW84iIRCbNi3vslUXKnCwvnw0GwwaQogYt3/ve9/C9730P3/zmN1FeXo76+nq8/vrr+O53vwsA2LFjBwvPEdEgla69Y9IfCMXbiZnF49Kj915TubryStSeLF26FOPGjcPWrVuxb98+mM1m/PznP8dFF10EAKipqQnWcSEiGkxSs3eMgKY2B6wtjp4ARYHDFluSgVDyQU6slUWDYQpDPGf2mpLa6FyiRA+/LrroomCQQkREfgO/uPtHamob7LDbXcEAJblAqH+jPfFWFrF4XPr03msqF4katLjdbjz99NPYuHEjGhsbUVpaigULFuCWW26BWq0Ws2lERKIa6N4xgZEanc6/0EEQgKOWDrjcPqiVZ2pgxQqE+j/aE31lUa6Wl6fMEPVT8stf/hJ79uzBqlWrUFlZCYvFgrVr18Jut+Puu+8Ws2lERKIa6MU90kiNSimHxxMatMQKhAY22hPtG39ulpePTZoJ1dlI1KBl69at2LhxI4qLiwEAo0aNwsSJE7FgwQIGLUQ0yA3s4h5pJYnD2Y1p48w4dKI1oUAoudGeZC7MyU5hxHvuSPdni3QlVA9Oor6zQt8QPs7tRESDS//zEwIjNbUNdv8zyYBxw42orjSgyqxPKLhIfLQnnRfm+DVfIt1fUmIIex4xRjtSk1BNAaIGLZdffjluvfVW/OhHP0JlZSVOnTqFp59+GpdffrmYzSIiygH+kZoxw42wNNj65JXIE7xgJjbak84Lc7znjnb/mOHGXs8i3mgHV0ullqhBy5133omnn34aq1evRmNjI8rKyjBv3jwsW7ZMzGYREeUIGUqKdBDcAynSGX+0J50X5njPHe3+js5uGNQKAOKOdgw0oZpCZTxo+eijj0L+PWvWLMyaNSvktk8//RTnnXdeJptFRET9lM4Lc7znjnZ/Qb46GKyJOdqRW6ulxE8ozvirds8990S8ve9uz++8804mm0VERP2UzgtzvOeOdr+pUIumJn8+j7ijHbmyWio7EoozHrS8++67mT4lERENWKxv2em8MPufu7xYh9ZOF7xewFSgDru/77llvZZOiT/aIf2Cb9mSUCzF8SkiIhqwZIb6E/mWnd4Lc32rI8b54517IEGV+FMi2SBbEorl8Q+Rpo0bN+LKK6/ExIkT8cILL8Q89tVXX8WcOXNQU1OD1atXB3eZJiLKTf4g5N1P67BzXz3e/bQOhy0dAAT4L9JuWFscsDndCFy0I33Ltjk9GWltas7vD2wqjIGRgcQCluiv0+CSLTtI52zQMmHCBDz22GOYP39+zOPq6urw1FNP4ZVXXsG2bdtw/Phx/P3vf89QK4mIMi9aEGB3eiJepOPt2pxuYp1f7GAtmwSm2AKBi1gJxTk7PTR27FgAgFweOy576623UFNTA6PRv6Z/0aJFeP3113H11Venu4lERKKIFgS0droiXqTPm1Ip6rJdsRJps2VKJLX6O92VHQnFORu0JMpqtaKysjL478rKSlit1qSfx2TSp7JZGWc2960eOTiw34ML++0nUymgP94aFgSoVMrgBou96bRKzJxcif3HzuSUTBxpwsiq4pCE13QpEQTMdHmTPv9A3+9or1NlmQElRboBPXc6Reu3IAjYc7gp7HWcWl2S8PtoTmVD+0GyQcvChQthsVgi3vfhhx9CoVBktD3NzXb4fNKc5zSbDTh92iZ2MzKO/R5c2O/eBIwo04cltuar5XA4XGEXacEroLJIA8P40pBv2YElxZmQ7PlT835Hfp0EtyfNn6X+J//G6rfN6cauLywh7++uLywwaBRZM3Ikl8tiDgJINmhZv359Sp6noqIiJPixWCyoqKhIyXMTEWWnaEP9iLE0WBY8JpBLktnpATGWDYsxJZK+eii5MN0l2aAlVebOnYvrr78ey5cvR1FREdatWxc3eZeISPoiBwHRL9LZUVws8zIbLKWzHkoubCmQs6uHNm3ahIsuughbt27F448/josuugiHDx8GADz++ON46aWXAABVVVVYtmwZrrnmGlx22WUYOnQorrrqKjGbTkQkoshLg6W9kiZ8GXe2SudKqWxZATQQ0mlpkubPnx91xOS2224L+ffixYuxePHiTDSLiEiSBj61IFaRNmmNEKV3NCQ7VgANRM4GLURElDoDu5iKFzhkS/n5RKV/ywFpbynAoIWIiOIayMVUzMAhPcmn6Rw1kv5oSDoxaCEiogT0/2Iq5qqV1E+3ZGLUSNqjIemUs4m4RESUav3Zv0fcfWtSnXzad9RIIZfhZKMdtQ2dWZ/kG5l0kpQBjrQQEVGapT9PI5bUTrf0HjVSKmSQK+T45EADTjbaYdCpEhx1yZado+ONGmVLO89g0EJERGkmdp5G6qZbek835evU2HWgAYJPgFqlSDBXJ3tWM8XONVJmTTt74/QQERFlQP+mlrJN7+kmt9sHwSfAXKyDWum/nMarqZJN9W5i5RplUzt740gLERFRws6MGrV1utDR6YJSceb7f7xcnb7TS/k6NdxuH9o6XRmffomVpJytJf8ZtBARESUlMN2khGusOalcnUCgoJD782EC00sdnS64xpozOv0SL9coG0v+M2ghIqIcI6CpzQFriyNF+TPRElKTz9UJBAonG+34pCdgMRfroFTIRSh6F7394iZPR8eghYiIcog/0bW2wQ673ZWCBNJ4ibPJJvn6AwWlQoGTjXaoVYqwfJhM72Qduf1iJ09HxkRcIiLKGalOIE1PQqoMpgINDDpVMGABsmP6JVT2JU8zaCEiIkityFg0qd4lOV27LufCjsti4KtDRDTopap2iPjFyFJdfTd9uy5n5/RLtmPQQkQ0yKVmQ8PsKJoWGMGobbAD6M8IRt/AS5HGhFTuMZQsBi1ERINcKmpyDCzwSeUIjX8EY8xwIywNtiSfL1rgZeCISJZg0EJENMilYgqk/4FPOkZoZCgp0kFwe5N6VLzAS/ojIuJP3w0UgxYiokEuFTU5+hv4pGZqKjWytQpsamTH9N1AMWghIhr0Bp4U2t/AJ3sCBQEKhRyOLg+USnlwKXJmlyGnbyQk+eAwO0dlGLQQEREGnhTav8AnfatzkuEfhTh4vAVFBRrsO9oMU6EWpgJNBpchp3ckJLngMHtHZVinhYiIUiReMbLwWjDZUK8kMArh9gjweX2YMaEMQ0v1OG9KZcYu1OneVTmZpeDZusMzwJEWIiLKiOjf3sWuV9J7FMLjFdBucwEAvF5fxtqR7mmyZKbvsmfKLhyDFiIiSrtEVuaIdUHMhimq9Lch8em7bHg9ouH0EBERpV26yuGnQjZMUfWvDcluvZDYXkLZ8HpEI34LiIgo52Xzt/fsKKmfbBsiT7eVlBhEaEvmMGghIqK0S0UtmPTKhpL6ibch2nTbmOHGjLclk7Ll00JERDkte7+9S1G06baOzm4Y1ApxGpUBDFqIiAa1TBYRy6Zv75nqd3rOE226rSBfnfT2BaGys6hcQM4GLRs3bsQf//hHHDlyBHfffTe+/e1vRzxu586d+MEPfoARI0YAANRqNdatW5fBlhIRiSV7i4ilV7r77b/wd3a50WJz4dCJ1pSfJ9p0m6lQi6Yme7/bne2fh5wNWiZMmIDHHnsMzzzzTNxjR48ejddffz0DrSIiyh7ZtO9PJqW332cu/AV6Df59oAGmQi2MBk2KzxN5uk3Wt4JcEqTwecjZoGXs2LEAALmcq7qJiCLJ5iJi6ZRYv/s3TdL7wu92++D1CTjd6oBeq4JaKU/x65va6TYpfB5yNmhJRm1tLRYuXAilUoklS5Zg4cKFYjeJiCjtsnsZcvrE73f/p0l6X/hVKjnkchl8PgHdbi/USjlUShkUCjmsLY6syxmRwudBskHLwoULYbFYIt734YcfQqFILHt60qRJ2LFjBwwGA+rq6nDDDTegrKwM559/flLtMZn0SR2fbczmVKztlx72e3Bhv0OVCAJmurzYf+zMxXniSBNGVhUPaJohW/S3301tDtQ22KHTaYKPqW2wY8xwI0qKdDHPKVMpoD/uz2GBTIbp48qw71gzDHoNCvVqFOnz8PmRJgCy4HmnVpek9PXu7+dcCp8HyQYt69evT8nz6PVngo2qqirU1NTgP//5T9JBS3OzHT5fvGqE2clsNuD0aZvYzcg49ntwYb8jqyzSwDC+NGQapP+JnNljIP22tjhgt7vCHmNpsEFwe+JMGwkYUaYPjtKolDLMP2848vNUUCjk+GivJWQkY9cXFhg0ipRNvwz0cy7250Eul8UcBJBs0JIqjY2NMJvNkMlkaGtrwwcffIDbbrtN7GYREWVINi1DzqTo/Y42TWLQqhKYNopej8ba4sj6nJFs/zzkbNCyadMmPPLII+jo6MA777yDZ555Bs899xyqq6vx+OOPo7S0FNdddx22bduGl156CUqlEl6vFwsWLEBNTY3YzSciIpFEW04sQEhwdU3kC78UckaynUwQ+sZ91B+cHpIe9ntwYb8Hl4H3O3z1kLXFiZ376sOOPHdSOSqMsXNdAs+Z7jooUn+/OT1ERESUtPDRkoGPlHArg4FiERMiIqIEBKaNAgtp+rfpoz8YqjAGppQYsCSDIy1EREQJiTZSAticbo6eZACDFiIiooT1nTbK/v16cgmnh4iIiPop2n49NqdH3IblKAYtRERE/dR3vx6lQoYCvQaW5k7YnG4A0lxVmq0YtBARUZYQYHO6YW1xSOaCH1hRBPgDFrlCjn8faMDnh5rw7qd1OGzpgBT6IRXMaSEioiwQnhsyZbQJ5iIt7E5P1ia49i5El69T498HGmAq1AZ3dI5cfI76i0ELERGJrm9uiEIuw8G6Nvzn4GkoFfIsTnA9s6LI0tyJ4eUFUCvPTGJkX5l+aeP0EBERia5vbki+To29R5rR1e0FkO0Jrv4VRZWmfGhUoZdV8cv0S2/KLRaOtBARkej6Vpt1u30QfALUKkXwmGwftYi2Z1FyxedSKfeWYzNoISIi0fW94KtVcpQZ80OmWsQftYgnu8r0R1uO7c+xUYbtrSSFQIZBCxERZYHQC75Bq8LQUn0WjVokKvIOz2LoO+UG+AOXzi43GlodkhyByfZ3n4iIBo3QC361NntGLaRBQFObA9YWB/RaFfRaZcQNHuVyeYwRGPGDrVgYtBARUZbKnlGL7CFEmdbx56/UNthht7uCS8Yj5dh4vb6IIzDZnC8UwKCFiIhIEqIn1gbyV3Q6jf9IAdh7pBnfOKcKZeeEjlbZnJ6IIzDJ5QtFC57Si0ELERGRBMRKrI2Wv2JzulFhDJ32GfgqJ/FWJTFoISIikoBogUlgtEPWJ16IPnoysFVOsVclpXd6icXliIiIJCBWYBIYPQncH3/0xJ8vdGYUJvERkljBU7pxpIWIiEgCYk/r+EdPxgw3wtJgS2ueSd9CgEDmaugwaCEiIpKEeNM6MpQU6SC4vWlthZiVfxm0EBFRzhEE/547uVfjJRuWgYtX+ZdBCxER5RgBew43YdcXFslVfJUOcYInJuISEVFOsTk92H8sfHVLdu4QTclg0EJERDlFzNUtlF4MWoiIKKckV7OEpIRBCxER5RSDVomJI5OpWUJSwXeQiIhyjAxTq0tg0ChycPXQ4JazQcuqVavw0UcfQa1WQ6fT4Z577sGUKVMiHvvqq6/iD3/4AwRBwEUXXYR7770XcjkHoYiIpEomy4alwZRqOXtlvuiii/DGG2/g73//O374wx/i9ttvj3hcXV0dnnrqKbzyyivYtm0bjh8/jr///e8Zbi0RERHFk7NBy6WXXgqVyh9hT5s2DfX19fD5fGHHvfXWW6ipqYHRaIRcLseiRYuwZcuWTDeXiIgoDn/BPGuLAzanG4AQ9xG5Jmenh3p78cUXcckll0Sc8rFaraisrAz+u7KyElarNZPNIyIiikPAYUtHWOn8zBXME2BzekTPEZJs0LJw4UJYLJaI93344YdQKBQAgM2bN+ONN97Aiy++mNb2mEz6tD5/upnNBrGbIAr2e3BhvweXXOp3U5sDtQ126HSa4G21DXaMGW5ESZEu5NhU91sQ/BWGAwX7ZDJg4kgTplaXQNZ3bXmaSTZoWb9+fdxj3n77bTz22GN4/vnnUVJSEvGYioqKkODHYrGgoqIi6fY0N9vh80lzqM5sNuD0aZvYzcg49ntwYb8Hl1zrt7XFAbvdFXa7pcEWskFiOvptc7qDWyIE7PrCAoNGkfJEZ7lcFnMQIGdzWt577z384he/wLPPPouhQ4dGPW7u3LnYvn07Wlpa4PP5sG7dOlxxxRUZbCkREVFsYhbMy6YKw5IdaYnnpz/9KVQqFVasWBG87fnnn0dxcTEef/xxlJaW4rrrrkNVVRWWLVuGa665BgBwwQUX4KqrrhKr2URERGEMWiUmjTKF5bRkomBeIGDqHbiIVWFYJgh94yfqD04PSQ/7Pbiw34NLbvY7fjJsevqduSTgeNNDOTvSQkRElFsiFcwLDWRK0jIOIUN1ZQHKinVcPURERET9ET4CMtPlRWWRBqkPKLKjwnDOJuISERHlMpvTEwxYAH/Oyf5jzbA5PeI2LI0YtBAREUlQalf1SKPaLqeHiIiIJCh1q3rErrabOI60EBERSVBgGXSgfkugUm2yy6AjTTPtO5qd00wcaSEiIspK8ZY4h6/qGVlVjKYme1JniTXNJHbibV8MWoiIiLJOolM2oat6+rMXUDYVj4uH00NERERZJpNTNpGmmTJVbTdZ2dciIiKiQS6zUzbZUzwuHgYtRESUAzJRGTZzMj9lkx3F4+Jh0EJERBKXycqwmSHmBonZbHD3noiIJC9aZVjD+NKsHzmITjpTNpnEoIWIiCRNSkt2kyONKZtM4uohIiKStED+R2/ZumSXBoZBCxERSVqqKsNS9uM7SkREEpeayrDiiVf5lgIYtBARUQ4YeGVYcUhns8JswOkhIiIikUhps8JswKCFiIhIJLFWPlE4Bi1EREQi4cqn5DBoISIiEomUNivMBnxViIiIRMPKt8lg0EJERCQqVr5NFKeHiIiISBIYtBAREZEkMGghIiIiSWDQQkRERJKQs4m4q1atwkcffQS1Wg2dTod77rkHU6ZMCTtu586d+MEPfoARI0YAANRqNdatW5fh1hIREVE8ORu0XHTRRbj77ruhUqnw3nvv4fbbb8f27dsjHjt69Gi8/vrrGW4hERERJSNng5ZLL700+PO0adNQX18Pn88HuZwzYkRERFKUs0FLby+++CIuueSSqAFLbW0tFi5cCKVSiSVLlmDhwoVJn0Mul3YhIKm3v7/Y78GF/R5c2G/pidd2mSD03apJGhYuXAiLxRLxvg8//BAKhQIAsHnzZjzxxBN48cUXUVJSEnas3W6HIAgwGAyoq6vDDTfcgNWrV+P8889Pa/uJiIgoOZINWhLx9ttvY82aNXj++ecxdOjQhB7z8MMPQ6/XY/ny5WluHRERESUjZxM83nvvPfziF7/As88+GzNgaWxsRCBua2trwwcffIDx48dnqplERESUoJwdafna174GlUoFo9EYvO35559HcXExHn/8cZSWluK6667DCy+8gJdeeglKpRJerxcLFizA0qVLRWw5ERERRZKzQQsRERHllpydHiIiIqLcwqCFiIiIJIFBCxEREUkCgxYiIiKSBAYtREREJAkMWgahjRs34sorr8TEiRPxwgsvRD1u586dOOuss7BgwQIsWLAAixYtymArUy/RfgPAq6++ijlz5qCmpgarV6+Gz+fLUCtTz+l04ic/+QnmzJmDyy+/HO+9917E43Lh/T527BiuvfZazJ07F9deey1qa2vDjvF6vVi1ahVqamowZ86cnNjVPZF+P/nkkzjvvPOC7++qVasy39AUW7NmDWbPno1x48bhq6++inhMLr7fifQ7F99vAIBAg87BgweFQ4cOCXfeeafwl7/8JepxH3/8sbBw4cIMtiy9Eu33iRMnhAsvvFBobm4WvF6vcOONNwrr16/PXENT7MknnxTuvvtuQRAE4dixY8L5558v2O32sONy4f3+zne+I2zYsEEQBEHYsGGD8J3vfCfsmPXr1ws33nij4PV6hebmZuHCCy8U6urqMt3UlEqk30888YTw8MMPZ7ppabVr1y7BYrEIl156qXDw4MGIx+Ti+51Iv3Px/RYEQeBIyyA0duxYVFdXD7odrxPt91tvvYWamhoYjUbI5XIsWrQIW7ZsyVArU+/NN9/E4sWLAQAjRozA5MmT8f7774vcqtRrbm7G/v37MX/+fADA/PnzsX//frS0tIQct2XLFixatAhyuRxGoxE1NTXYunWrGE1OiUT7nYtmzJiBioqKmMfk2vsNJNbvXDW4rlqUtMAO2IsWLcL69evFbk5GWK1WVFZWBv9dWVkJq9UqYosGxmKxYMiQIcF/V1RUoL6+PuKxUn6/rVYrysrKgpulKhQKlJaWhr13fd/fWK+HFCTab8C/geyVV16JG2+8Ebt37850U0WRa+93MnLx/VaK3QBKvUR3wI5n0qRJ2LFjR8gO2GVlZVm7A3aq+i018fqdKKm935ScxYsX45ZbboFKpcIHH3yAZcuWYcuWLSguLha7aZQGufp+M2jJQan6hqzX64M/V1VVoaamBv/5z3+y9iKWqn5XVFSEBAEWiyWrh2Lj9buyshKnTp0K7sNltVpx7rnnhh0ntfe7r4qKCjQ0NMDr9UKhUMDr9aKxsTHsvQu8v1OnTgUQ/k1cahLtt9lsDv58wQUXoKKiAocOHcKsWbMy3eSMyrX3O1G5+n5zeoiiGqw7YM+dOxfbt29HS0sLfD4f1q1bhyuuuELsZvXb5ZdfjldeeQWAf/pn7969uPDCC8OOk/r7bTKZMGHCBGzatAkAsGnTJkyYMCFk01TA/3qsW7cOPp8PLS0t2L59O+bOnStGk1Mi0X43NDQEfz5w4ABOnTqFkSNHZrStYsi19ztRufp+c8PEQWjTpk145JFH0NHRAZVKBa1Wi+eeew7V1dU5vQN2ov0GgJdffhl//OMfAfi/pdx3332SnV5yOBxYuXIlDhw4ALlcjjvvvBM1NTUAkHPv95EjR7By5Up0dHSgoKAAa9aswahRo7B06VKsWLECU6ZMgdfrxerVq/HBBx8AAJYuXYprr71W5JYPTCL9vuuuu7Bv3z7I5XKoVCqsWLECF198sdhNH5AHH3wQ27ZtQ1NTE4qLi1FUVITNmzfn/PudSL9z8f0GGLQQERGRRHB6iIiIiCSBQQsRERFJAoMWIiIikgQGLURERCQJDFqIiIhIEhi0EBERkSQwaCEiIiJJYNBCRJLj8XjEbgIRiYBBCxFJwuzZs/HMM8/gyiuvxLRp07B27VrU1NRg+vTpmDdvHt5+++3gsa+//jquu+46rFmzBjNnzsTs2bOxY8eO4P11dXW4/vrrMX36dHz/+9/HqlWrcMcddwTv/+yzz7B48WLMmDEDV111FXbu3JnRvhJRZAxaiEgyNm/ejGeeeQb//ve/MXLkSLz44ov49NNPsXz5ctx5551obGwMHrtnzx6MHDkSH3/8MW6++Wbcc889wb2V7rjjDkydOhU7d+7E8uXLsXHjxuDjGhoa8MMf/hC33norPvnkE9x1111YsWIFWlpaMt5fIgrFoIWIJOM73/kOKioqkJeXhyuuuAJlZWWQy+WYN28ehg8fjj179gSPraysxDXXXAOFQoGFCxfi9OnTaGpqgsViwd69e7FixQqo1WrMmDEDs2fPDj5u48aNuOiii3DxxRdDLpfjggsuwOTJk0NGaohIHEqxG0BElKiKiorgzxs2bMCf/vQnnDp1CoB/Y8jW1tbg/SUlJcGftVptyDGFhYXB2wLPa7VaAQAWiwVbt27Fe++9F7zf4/Hg3HPPTU+niChhDFqISDJkMhkA4NSpU7j33nvx/PPPY/r06VAoFFiwYEFCz2E2m9He3g6n0xkMXAIBC+APYBYsWIAHH3ww9R0gogHh9BARSY7T6YRMJoPRaAQAvPbaazh06FBCjx0yZAgmT56MJ598Et3d3di9e3fIqMpVV12F9957D//85z/h9Xrhcrmwc+dO1NfXp6UvRJQ4Bi1EJDnV1dW48cYbsXjxYpx//vn46quvcPbZZyf8+F/96lf47LPPcO655+I3v/kN5s2bB7VaDcA/0rJ27Vr8/ve/x3nnnYeLL74Yzz77LHw+X7q6Q0QJkgmBdHoiokHqJz/5CUaNGoUVK1aI3RQiioEjLUQ06OzZswcnTpyAz+fD+++/j3feeQc1NTViN4uI4mAiLhENOk1NTfjxj3+MtrY2lJeX44EHHsDEiRPFbhYRxcHpISIiIpIETg8RERGRJDBoISIiIklg0EJERESSwKCFiIiIJIFBCxEREUkCgxYiIiKShP8fYyqfZJUpjDkAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 576x432 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (std_ax, joint_ax) = plt.subplots(\n",
" nrows=2, sharex=True, sharey=False,\n",
" gridspec_kw={'height_ratios': [1, 4]}\n",
")\n",
"\n",
"sns.scatterplot(x=\"range\", y=\"logratio\", data=std_df,\n",
" alpha=0.5, ax=joint_ax);\n",
"\n",
"(std_df.groupby(std_df[\"range\"].round(1))\n",
" [\"logratio\"]\n",
" .std()\n",
" .rolling(5)\n",
" .mean()\n",
" .plot(ax=std_ax));\n",
"\n",
"std_ax.set_ylabel(\"Standard\\ndeviation\\n(binned)\");\n",
"\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"id": "bb863b2d",
"metadata": {},
"source": [
"The scatter plot shows that the relationship is definitely nonlinear, and there is no obvious (to me at least) transform of `logratio` that will make the relationship linear. The top plot shows how the (binned, smoothed) standard deviation of `logratio` varies with `range`. As is evident from both plots, as `range` increases, so does the scale of variation of `logratio`."
]
},
{
"cell_type": "markdown",
"id": "a1c8ec2b",
"metadata": {},
"source": [
"## Introduction to Splines\n",
"\n",
"Regression splines are a type of of [generalized additive model](https://en.wikipedia.org/wiki/Generalized_additive_model) (GAM) that use linear combinations of (generally low-degree) polynomials to introduce nonlinear relationships between covariates and responses.\n",
"\n",
"To begin constructing our spline model, we must choose a number of knots (also known as anchors or control points) in the domain of our co variate. In this post we will use twenty splines in the interval $[-1.75, 1.75]$, which comfortably contains the observed values of `range`."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "7bacc150",
"metadata": {},
"outputs": [],
"source": [
"N_KNOT = 20\n",
"\n",
"knots = np.linspace(-1.75, 1.75, N_KNOT)"
]
},
{
"cell_type": "markdown",
"id": "21b69149",
"metadata": {},
"source": [
"The following plot shows the location of the knots in the Lidar data."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "31b0d1b3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x432 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (std_ax, joint_ax) = plt.subplots(\n",
" nrows=2, sharex=True, sharey=False,\n",
" gridspec_kw={'height_ratios': [1, 4]}\n",
")\n",
"\n",
"sns.scatterplot(x=\"range\", y=\"logratio\", data=std_df,\n",
" alpha=0.5, ax=joint_ax);\n",
"sns.rugplot(knots, height=0.075,\n",
" c='k', label=\"Knots\",\n",
" ax=joint_ax);\n",
"\n",
"(std_df.groupby(std_df[\"range\"].round(1))\n",
" [\"logratio\"]\n",
" .std()\n",
" .rolling(5)\n",
" .mean()\n",
" .plot(ax=std_ax));\n",
"sns.rugplot(knots, height=0.15,\n",
" c='k', label=\"Knots\",\n",
" ax=std_ax);\n",
"\n",
"std_ax.set_ylabel(\"Standard\\ndeviation\\n(binned)\");\n",
"\n",
"joint_ax.legend();\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"id": "b150c97f",
"metadata": {},
"source": [
"Let $x^*_i$, $i = 1, 2, \\ldots, 20$ be the location of the $j$-th knot. The spline model we will use is given by\n",
"\n",
"$$E(Y\\ |\\ X) = \\sum_{j = 1}^{20} \\beta_j \\cdot B_{j, k; \\mathbf{x}^*}(X)$$.\n",
"\n",
"(If one applies a link function to the conditional expectation of the left hand side, this becomes a _generalized_ additive model.) For spline regression, $B_{j, k; \\mathbf{x}^*}(\\cdot)$ is a $k$-th-degree polynomial in $x$ and $x^*$. There are many possible choices for these functions. We will use `scipy`'s cubic [B-spline](https://en.wikipedia.org/wiki/B-spline) [implementation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.html). For more information splines, consult Simon Wood's excellent book [_Generalized Additive Models_](https://www.taylorfrancis.com/books/mono/10.1201/9781315370279/generalized-additive-models-simon-wood)."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "0b1d711e",
"metadata": {},
"outputs": [],
"source": [
"basis = sp.interpolate.BSpline(knots, np.eye(N_KNOT), 3)"
]
},
{
"cell_type": "markdown",
"id": "710d28f7",
"metadata": {},
"source": [
"We see that `basis` is a callable function function that will give the design matrix for spline regression at a given set of points."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "a8c7394a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hasattr(basis, '__call__')"
]
},
{
"cell_type": "markdown",
"id": "9b6df33e",
"metadata": {},
"source": [
"We build this design matrix at the (standardized) value of `range`."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "8d49dd96",
"metadata": {},
"outputs": [],
"source": [
"dmat = shared(basis(std_df[\"range\"]))"
]
},
{
"cell_type": "markdown",
"id": "0f406f45",
"metadata": {},
"source": [
"With `dmat` in hand, we are ready to build our model with `pymc3`. We follow the model specified in [Milad Kharratzadeh's](http://www.miladkh.com/) excellent short paper [_Splines in Stan_](https://github.com/milkha/Splines_in_Stan/blob/master/splines_in_stan.pdf)."
]
},
{
"cell_type": "markdown",
"id": "7a917bf9",
"metadata": {},
"source": [
"The model for the conditional mean is given above,\n",
"\n",
"$$\\mu\\ |\\ X = \\sum_{j = 1}^{20} \\beta_j \\cdot B_{j, k; \\mathbf{x}^*}(X).$$\n",
"\n",
"We put a Gaussian random walk prior (GRW) on these coefficients $\\beta_j$, under the intuition that the coefficients for adjacent knots should be similar. We parameterize our GRW as follows:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" \\mu_{\\beta}\n",
" & \\sim N(0, 2.5^2) \\\\\n",
" \\Delta_{\\beta, j}\n",
" & \\sim N(0, 1) \\\\\n",
" \\sigma_{\\beta}\n",
" & \\sim \\mathrm{Half}-N(2.5^2) \\\\\n",
" \\beta_j\n",
" & = \\mu_{\\beta} + \\sigma_{\\beta} \\cdot \\sum_{i = 1}^j \\Delta_{\\beta, i}.\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "168f5b42",
"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)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "7194b51e",
"metadata": {},
"outputs": [],
"source": [
"coords = {\"knot\": np.arange(N_KNOT)}\n",
"\n",
"with pm.Model(coords=coords) as model:\n",
" μ_β = pm.Normal(\"μ_β\", 0., 2.5)\n",
" Δ_β = pm.Normal(\"Δ_β\", 0., 1., dims=\"knot\")\n",
" σ_β = pm.HalfNormal(\"σ_β\", 2.5 * HALFNORMAL_SCALE)\n",
" β = pm.Deterministic(\"β\", μ_β + σ_β * Δ_β.cumsum(),\n",
" dims=\"knot\")\n",
" μ = at.dot(dmat, β)"
]
},
{
"cell_type": "markdown",
"id": "38f97e66",
"metadata": {},
"source": [
"Our observational model here is normal, with unknown variance $\\sigma \\sim \\mathrm{Half-}N(2.5^2)$."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "5bc86693",
"metadata": {},
"outputs": [],
"source": [
"with model:\n",
" σ = pm.HalfNormal(\"σ\", 2.5 * HALFNORMAL_SCALE)\n",
" obs = pm.Normal(\"obs\", μ, σ, observed=std_df[\"logratio\"])"
]
},
{
"cell_type": "markdown",
"id": "7c378bd1",
"metadata": {},
"source": [
"We now sample from the posterior distribution of this model."
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "6ef76956",
"metadata": {},
"outputs": [],
"source": [
"SEED = 123456789\n",
"CORES = 3\n",
"\n",
"SAMPLE_KWARGS = {\n",
" 'cores': CORES,\n",
" 'random_seed': [SEED + i for i in range(CORES)],\n",
" 'return_inferencedata': True,\n",
" 'target_accept': 0.95\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "84f16daf",
"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: [μ_β, Δ_β, σ_β, σ]\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 02:21<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 142 seconds.\n"
]
}
],
"source": [
"with model:\n",
" trace = pm.sample(**SAMPLE_KWARGS)"
]
},
{
"cell_type": "markdown",
"id": "1f87ab00",
"metadata": {},
"source": [
"None of the standard sampling diagnostics show cause for concern."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "735649a7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_energy(trace);"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "251ce43b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
"<defs>\n",
"<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
"<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
"<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
"<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
"</symbol>\n",
"<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
"<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
"<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
"<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
"<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
"</symbol>\n",
"</defs>\n",
"</svg>\n",
"<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
" *\n",
" */\n",
"\n",
":root {\n",
" --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
" --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
" --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
" --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
" --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
" --xr-background-color: var(--jp-layout-color0, white);\n",
" --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
" --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
"}\n",
"\n",
"html[theme=dark],\n",
"body.vscode-dark {\n",
" --xr-font-color0: rgba(255, 255, 255, 1);\n",
" --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
" --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
" --xr-border-color: #1F1F1F;\n",
" --xr-disabled-color: #515151;\n",
" --xr-background-color: #111111;\n",
" --xr-background-color-row-even: #111111;\n",
" --xr-background-color-row-odd: #313131;\n",
"}\n",
"\n",
".xr-wrap {\n",
" display: block;\n",
" min-width: 300px;\n",
" max-width: 700px;\n",
"}\n",
"\n",
".xr-text-repr-fallback {\n",
" /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
" display: none;\n",
"}\n",
"\n",
".xr-header {\n",
" padding-top: 6px;\n",
" padding-bottom: 6px;\n",
" margin-bottom: 4px;\n",
" border-bottom: solid 1px var(--xr-border-color);\n",
"}\n",
"\n",
".xr-header > div,\n",
".xr-header > ul {\n",
" display: inline;\n",
" margin-top: 0;\n",
" margin-bottom: 0;\n",
"}\n",
"\n",
".xr-obj-type,\n",
".xr-array-name {\n",
" margin-left: 2px;\n",
" margin-right: 10px;\n",
"}\n",
"\n",
".xr-obj-type {\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-sections {\n",
" padding-left: 0 !important;\n",
" display: grid;\n",
" grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
"}\n",
"\n",
".xr-section-item {\n",
" display: contents;\n",
"}\n",
"\n",
".xr-section-item input {\n",
" display: none;\n",
"}\n",
"\n",
".xr-section-item input + label {\n",
" color: var(--xr-disabled-color);\n",
"}\n",
"\n",
".xr-section-item input:enabled + label {\n",
" cursor: pointer;\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-section-item input:enabled + label:hover {\n",
" color: var(--xr-font-color0);\n",
"}\n",
"\n",
".xr-section-summary {\n",
" grid-column: 1;\n",
" color: var(--xr-font-color2);\n",
" font-weight: 500;\n",
"}\n",
"\n",
".xr-section-summary > span {\n",
" display: inline-block;\n",
" padding-left: 0.5em;\n",
"}\n",
"\n",
".xr-section-summary-in:disabled + label {\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-section-summary-in + label:before {\n",
" display: inline-block;\n",
" content: '►';\n",
" font-size: 11px;\n",
" width: 15px;\n",
" text-align: center;\n",
"}\n",
"\n",
".xr-section-summary-in:disabled + label:before {\n",
" color: var(--xr-disabled-color);\n",
"}\n",
"\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",
" μ_β float64 1.002\n",
" Δ_β float64 1.003\n",
" σ_β float64 1.003\n",
" σ float64 1.001\n",
" β float64 1.002</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-6be9e327-8217-444b-82ac-8d72e31b9762' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-6be9e327-8217-444b-82ac-8d72e31b9762' 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-262c20ca-f234-455e-a412-57ae50add49d' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-262c20ca-f234-455e-a412-57ae50add49d' 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-4159528f-614b-4383-9914-6f8a2ee6919b' class='xr-section-summary-in' type='checkbox' checked><label for='section-4159528f-614b-4383-9914-6f8a2ee6919b' class='xr-section-summary' >Data variables: <span>(5)</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>μ_β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.002</div><input id='attrs-e3ef8664-98c0-491b-9e90-f9df14021341' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e3ef8664-98c0-491b-9e90-f9df14021341' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3cc66f89-032b-4da6-90dc-c9f43e377ae6' class='xr-var-data-in' type='checkbox'><label for='data-3cc66f89-032b-4da6-90dc-c9f43e377ae6' 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(1.00177301)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.003</div><input id='attrs-f7d29b36-94b4-49ae-8a0a-604226555c27' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f7d29b36-94b4-49ae-8a0a-604226555c27' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-788b1891-2d2f-470c-831c-6e0f03a8efb6' class='xr-var-data-in' type='checkbox'><label for='data-788b1891-2d2f-470c-831c-6e0f03a8efb6' 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(1.00304857)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.003</div><input id='attrs-44f8d525-edee-4f7b-911c-81dfb07460b6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-44f8d525-edee-4f7b-911c-81dfb07460b6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f79ac85a-eba8-4c81-a547-6d99db461896' class='xr-var-data-in' type='checkbox'><label for='data-f79ac85a-eba8-4c81-a547-6d99db461896' 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(1.00278469)</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-e981d8e5-65ab-4f10-b947-5976f10b9c2e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e981d8e5-65ab-4f10-b947-5976f10b9c2e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-902e30d3-d247-469e-99db-87992ac032a3' class='xr-var-data-in' type='checkbox'><label for='data-902e30d3-d247-469e-99db-87992ac032a3' 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(1.00087722)</pre></div></li><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'>1.002</div><input id='attrs-e31c6ee9-83ae-44b9-a2a2-ae7915a5da0e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e31c6ee9-83ae-44b9-a2a2-ae7915a5da0e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6b553585-f795-42a2-9667-242dc6c723e9' class='xr-var-data-in' type='checkbox'><label for='data-6b553585-f795-42a2-9667-242dc6c723e9' 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(1.00209198)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-879965fa-b95c-4639-8d79-138f8d4b19dd' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-879965fa-b95c-4639-8d79-138f8d4b19dd' 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",
" μ_β float64 1.002\n",
" Δ_β float64 1.003\n",
" σ_β float64 1.003\n",
" σ float64 1.001\n",
" β float64 1.002"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.rhat(trace).max()"
]
},
{
"cell_type": "markdown",
"id": "82d7f8f1",
"metadata": {},
"source": [
"To visualize our predictions, we sample from the posterior predictive distribution along a grid of reasonable values for `range`."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "939c1bce",
"metadata": {},
"outputs": [],
"source": [
"pp_range = np.linspace(-1.75, 1.75, 100)\n",
"dmat.set_value(basis(pp_range))"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "88a0091d",
"metadata": {},
"outputs": [
{
"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='3000' class='' max='3000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [3000/3000 00:00<00:00]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with model:\n",
" pp_trace = pm.sample_posterior_predictive(trace)"
]
},
{
"cell_type": "markdown",
"id": "c315bb69",
"metadata": {},
"source": [
"We now plot the posterior predictions."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "b76bc7b2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x432 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (std_ax, joint_ax) = plt.subplots(\n",
" nrows=2, sharex=True, sharey=False,\n",
" gridspec_kw={'height_ratios': [1, 4]}\n",
")\n",
"\n",
"low, high = np.percentile(pp_trace[\"obs\"], [2.5, 97.5], axis=0)\n",
"joint_ax.fill_between(pp_range, low, high,\n",
" color='k', alpha=0.25,\n",
" label=\"95% credible interval\");\n",
"\n",
"sns.scatterplot(x=\"range\", y=\"logratio\", data=std_df,\n",
" alpha=0.5, ax=joint_ax);\n",
"\n",
"(std_df.groupby(std_df[\"range\"].round(1))\n",
" [\"logratio\"]\n",
" .std()\n",
" .rolling(5)\n",
" .mean()\n",
" .plot(ax=std_ax, label=\"Actual\"));\n",
"\n",
"std_ax.plot(pp_range, pp_trace[\"obs\"].std(axis=0),\n",
" c='k', label=\"Posterior predictive\");\n",
"\n",
"joint_ax.plot(pp_range, pp_trace[\"obs\"].mean(axis=0),\n",
" c='k', label=\"Posterior expected value\");\n",
"\n",
"std_ax.set_ylabel(\"Standard\\ndeviation\\n(binned)\");\n",
"\n",
"std_ax.legend(loc='upper left', bbox_to_anchor=(0., 1.65));\n",
"joint_ax.legend(loc='lower left');\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"id": "08c6bb9f",
"metadata": {},
"source": [
"Visually, we appear to have captured the relationship between `range` and the expected value of `logratio` reasonably well. The credible interval and the standard deviation above are a bit odd though. We have built a homoskedastic (same-variance) observational model, so the credible interval has roughly the same width, even though the data show a small variance for small values of range, and variance increases as `range` does."
]
},
{
"cell_type": "markdown",
"id": "25859eda",
"metadata": {},
"source": [
"### Accounting for heteroskedasticity\n",
"\n",
"In order to remedy this issue, we will build a heteroskedastic model that allows the variance of `logratio` to vary with `ratio`. In fact, we will use a spline to model the changing variance as well.\n",
"\n",
"Let $\\gamma_j$ come from a GRW similar to $\\beta_j$. We define\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" \\eta_{\\sigma}\\ |\\ X\n",
" & = \\sum_{j = 1}^{20} \\gamma_j \\cdot B_{j, k; \\mathbf{x}^*}(X) \\\\\n",
" \\sigma\\ |\\ X\n",
" & = 0.05 + \\exp(\\eta_{\\sigma}).\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Note that the $0.05$ factor in the definition of $\\sigma\\ |\\ X$ sets a lower bound on the variance, which is necessary for computational stability.\n",
"\n",
"The model is a straightforward adaptation of the homoskedastic one."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "d32acafd",
"metadata": {},
"outputs": [],
"source": [
"dmat.set_value(basis(std_df[\"range\"]))"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "701b5a5f",
"metadata": {},
"outputs": [],
"source": [
"with pm.Model(coords=coords) as var_model:\n",
" β0 = pm.Normal(\"β0\", 0., 2.5)\n",
" Δ_β = pm.Normal(\"Δ_β\", 0., 1., dims=\"knot\")\n",
" σ_β = pm.HalfNormal(\"σ_β\", 2.5 * HALFNORMAL_SCALE)\n",
" β = pm.Deterministic(\"β\", β0 + Δ_β.cumsum() * σ_β,\n",
" dims=\"knot\")\n",
" μ = at.dot(dmat, β)\n",
" \n",
" γ0 = pm.Normal(\"γ0\", 0., 2.5)\n",
" Δ_γ = pm.Normal(\"Δ_γ\", 0., 1., dims=\"knot\")\n",
" σ_γ = pm.HalfNormal(\"σ_γ\", 2.5 * HALFNORMAL_SCALE)\n",
" γ = pm.Deterministic(\"γ\", γ0 + Δ_γ.cumsum() * σ_γ,\n",
" dims=\"knot\")\n",
" η_σ = at.dot(dmat, γ)\n",
" σ = 0.05 + at.exp(η_σ)\n",
"\n",
" obs = pm.Normal(\"obs\", μ, σ, observed=std_df[\"logratio\"])"
]
},
{
"cell_type": "markdown",
"id": "8e932347",
"metadata": {},
"source": [
"We now sample from this model."
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "22abd331",
"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: [β0, Δ_β, σ_β, γ0, Δ_γ, σ_γ]\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 04:42<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 282 seconds.\n"
]
}
],
"source": [
"with var_model:\n",
" var_trace = pm.sample(**SAMPLE_KWARGS)"
]
},
{
"cell_type": "markdown",
"id": "5add4654",
"metadata": {},
"source": [
"Again the sampling diagnostics show no cause for concern."
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "99856df5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_energy(var_trace);"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "1874aad7",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
"<defs>\n",
"<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
"<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
"<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
"<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
"</symbol>\n",
"<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
"<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
"<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
"<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
"<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
"</symbol>\n",
"</defs>\n",
"</svg>\n",
"<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
" *\n",
" */\n",
"\n",
":root {\n",
" --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
" --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
" --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
" --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
" --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
" --xr-background-color: var(--jp-layout-color0, white);\n",
" --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
" --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
"}\n",
"\n",
"html[theme=dark],\n",
"body.vscode-dark {\n",
" --xr-font-color0: rgba(255, 255, 255, 1);\n",
" --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
" --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
" --xr-border-color: #1F1F1F;\n",
" --xr-disabled-color: #515151;\n",
" --xr-background-color: #111111;\n",
" --xr-background-color-row-even: #111111;\n",
" --xr-background-color-row-odd: #313131;\n",
"}\n",
"\n",
".xr-wrap {\n",
" display: block;\n",
" min-width: 300px;\n",
" max-width: 700px;\n",
"}\n",
"\n",
".xr-text-repr-fallback {\n",
" /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
" display: none;\n",
"}\n",
"\n",
".xr-header {\n",
" padding-top: 6px;\n",
" padding-bottom: 6px;\n",
" margin-bottom: 4px;\n",
" border-bottom: solid 1px var(--xr-border-color);\n",
"}\n",
"\n",
".xr-header > div,\n",
".xr-header > ul {\n",
" display: inline;\n",
" margin-top: 0;\n",
" margin-bottom: 0;\n",
"}\n",
"\n",
".xr-obj-type,\n",
".xr-array-name {\n",
" margin-left: 2px;\n",
" margin-right: 10px;\n",
"}\n",
"\n",
".xr-obj-type {\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-sections {\n",
" padding-left: 0 !important;\n",
" display: grid;\n",
" grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
"}\n",
"\n",
".xr-section-item {\n",
" display: contents;\n",
"}\n",
"\n",
".xr-section-item input {\n",
" display: none;\n",
"}\n",
"\n",
".xr-section-item input + label {\n",
" color: var(--xr-disabled-color);\n",
"}\n",
"\n",
".xr-section-item input:enabled + label {\n",
" cursor: pointer;\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-section-item input:enabled + label:hover {\n",
" color: var(--xr-font-color0);\n",
"}\n",
"\n",
".xr-section-summary {\n",
" grid-column: 1;\n",
" color: var(--xr-font-color2);\n",
" font-weight: 500;\n",
"}\n",
"\n",
".xr-section-summary > span {\n",
" display: inline-block;\n",
" padding-left: 0.5em;\n",
"}\n",
"\n",
".xr-section-summary-in:disabled + label {\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-section-summary-in + label:before {\n",
" display: inline-block;\n",
" content: '►';\n",
" font-size: 11px;\n",
" width: 15px;\n",
" text-align: center;\n",
"}\n",
"\n",
".xr-section-summary-in:disabled + label:before {\n",
" color: var(--xr-disabled-color);\n",
"}\n",
"\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",
" β0 float64 0.9998\n",
" Δ_β float64 1.006\n",
" σ_β float64 1.0\n",
" γ0 float64 1.001\n",
" Δ_γ float64 1.005\n",
" σ_γ float64 1.0\n",
" β float64 1.002\n",
" γ float64 1.002</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-7362aa37-9f8a-4802-b82c-c036e0ce48e8' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7362aa37-9f8a-4802-b82c-c036e0ce48e8' 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-0c5a2fdc-6a32-4688-af4c-eb27e082d3d5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-0c5a2fdc-6a32-4688-af4c-eb27e082d3d5' 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-b29bc7b8-3e4e-4279-aac8-20d38dd7d09c' class='xr-section-summary-in' type='checkbox' checked><label for='section-b29bc7b8-3e4e-4279-aac8-20d38dd7d09c' class='xr-section-summary' >Data variables: <span>(8)</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>β0</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.9998</div><input id='attrs-1f5170ce-ccfc-4311-8246-d9e627ab323e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1f5170ce-ccfc-4311-8246-d9e627ab323e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-cd3e8eda-7d32-4aad-83e5-9d277c2f3e56' class='xr-var-data-in' type='checkbox'><label for='data-cd3e8eda-7d32-4aad-83e5-9d277c2f3e56' 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(0.99984598)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.006</div><input id='attrs-089a661f-4ba0-464e-97a8-dc623d98dca7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-089a661f-4ba0-464e-97a8-dc623d98dca7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9e4f120d-d01c-4a49-b8fb-3ae5672f9b45' class='xr-var-data-in' type='checkbox'><label for='data-9e4f120d-d01c-4a49-b8fb-3ae5672f9b45' 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(1.00613202)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_β</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.0</div><input id='attrs-551b992b-dfb9-4dc0-9da0-480350993952' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-551b992b-dfb9-4dc0-9da0-480350993952' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4149d6bf-ce6e-4073-bcdd-806b4ccd5069' class='xr-var-data-in' type='checkbox'><label for='data-4149d6bf-ce6e-4073-bcdd-806b4ccd5069' 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(1.00047073)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>γ0</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-12f3c607-8ac1-4f55-ac6e-407119acf580' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-12f3c607-8ac1-4f55-ac6e-407119acf580' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-38f8b3df-a0d6-45cf-ba57-2bca9b92d994' class='xr-var-data-in' type='checkbox'><label for='data-38f8b3df-a0d6-45cf-ba57-2bca9b92d994' 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(1.0010354)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>Δ_γ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.005</div><input id='attrs-790917a7-b6d6-4286-9eb9-f0e8100d6d30' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-790917a7-b6d6-4286-9eb9-f0e8100d6d30' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f01e1c18-b63b-40ad-825c-bfcf0e39f3a3' class='xr-var-data-in' type='checkbox'><label for='data-f01e1c18-b63b-40ad-825c-bfcf0e39f3a3' 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(1.00481044)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>σ_γ</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.0</div><input id='attrs-d4e97dad-29e0-4a7a-baf7-9f4eeb46dc58' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d4e97dad-29e0-4a7a-baf7-9f4eeb46dc58' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1afcb5f6-1ba2-481e-b828-aae93a973229' class='xr-var-data-in' type='checkbox'><label for='data-1afcb5f6-1ba2-481e-b828-aae93a973229' 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(1.00035778)</pre></div></li><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'>1.002</div><input id='attrs-4c219615-905a-408d-9278-74f6bcce7310' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4c219615-905a-408d-9278-74f6bcce7310' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-21ad6f14-44b1-40af-9a70-a205599bf077' class='xr-var-data-in' type='checkbox'><label for='data-21ad6f14-44b1-40af-9a70-a205599bf077' 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(1.00226144)</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'>1.002</div><input id='attrs-8c961902-eca0-4928-8bd5-1f83664db8a4' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8c961902-eca0-4928-8bd5-1f83664db8a4' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-26417bc1-f4bb-47f5-b133-2661c4174d78' class='xr-var-data-in' type='checkbox'><label for='data-26417bc1-f4bb-47f5-b133-2661c4174d78' 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(1.00190525)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-ec411289-4373-47ec-93b8-5f529dd60452' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-ec411289-4373-47ec-93b8-5f529dd60452' 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",
" β0 float64 0.9998\n",
" Δ_β float64 1.006\n",
" σ_β float64 1.0\n",
" γ0 float64 1.001\n",
" Δ_γ float64 1.005\n",
" σ_γ float64 1.0\n",
" β float64 1.002\n",
" γ float64 1.002"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.rhat(var_trace).max()"
]
},
{
"cell_type": "markdown",
"id": "fd4bc2ed",
"metadata": {},
"source": [
"We do see that the values of $\\gamma_j$ that correspond to small values of `range` have small coefficients, and the coefficients grow as `range` gets larger."
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "f03c3ed4",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x720 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax, = az.plot_forest(var_trace, var_names=[\"γ\"])\n",
"\n",
"ax.set_xlabel(r\"$\\gamma_j$\");\n",
"\n",
"ax.set_yticklabels(np.arange(N_KNOT)[::-1]);\n",
"ax.set_ylabel(\"$j$\");"
]
},
{
"cell_type": "markdown",
"id": "b05b9873",
"metadata": {},
"source": [
"Again we sample from the posterior predictive distribution of this model."
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "3b7f0eec",
"metadata": {},
"outputs": [],
"source": [
"dmat.set_value(basis(pp_range))"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "4b982329",
"metadata": {},
"outputs": [
{
"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='3000' class='' max='3000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [3000/3000 00:00<00:00]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with var_model:\n",
" pp_var_trace = pm.sample_posterior_predictive(var_trace)"
]
},
{
"cell_type": "markdown",
"id": "3059be67",
"metadata": {},
"source": [
"We plot these predictions in order to compare them to those of the homoskedastic model."
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "ffb4ade4",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x432 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (std_ax, joint_ax) = plt.subplots(\n",
" nrows=2, sharex=True, sharey=False,\n",
" gridspec_kw={'height_ratios': [1, 4]}\n",
")\n",
"\n",
"low, high = np.percentile(pp_var_trace[\"obs\"], [2.5, 97.5], axis=0)\n",
"joint_ax.fill_between(pp_range, low, high,\n",
" color='k', alpha=0.25,\n",
" label=\"95% credible interval\");\n",
"\n",
"sns.scatterplot(x=\"range\", y=\"logratio\", data=std_df,\n",
" alpha=0.5, ax=joint_ax);\n",
"\n",
"(std_df.groupby(std_df[\"range\"].round(1))\n",
" [\"logratio\"]\n",
" .std()\n",
" .rolling(5)\n",
" .mean()\n",
" .plot(ax=std_ax, label=\"Actual\"));\n",
"\n",
"std_ax.plot(pp_range, pp_trace[\"obs\"].std(axis=0),\n",
" c='k', label=\"Posterior predictive\\n(homoskedastic)\");\n",
"std_ax.plot(pp_range, pp_var_trace[\"obs\"].std(axis=0),\n",
" c='r', ls='--',\n",
" label=\"Posterior predictive\\n(heteroskedastic)\");\n",
"\n",
"joint_ax.plot(pp_range, pp_trace[\"obs\"].mean(axis=0),\n",
" c='k', label=\"Posterior predictive\\n(homoskedastic)\");\n",
"joint_ax.plot(pp_range, pp_var_trace[\"obs\"].mean(axis=0),\n",
" c='r', ls='--',\n",
" label=\"Posterior predictive\\n(heteroskedastic)\");\n",
"\n",
"std_ax.set_ylabel(\"Standard\\ndeviation\\n(binned)\");\n",
"\n",
"std_ax.legend(loc='upper left', ncol=3,\n",
" bbox_to_anchor=(0., 1.6));\n",
"joint_ax.legend(loc='lower left');\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"id": "2a206bf1",
"metadata": {},
"source": [
"We see that the homo- and heteroskedastic models produce essentially the same estimate of the expected value of `logratio`, but that the heteroskedastic model comes closer to capturing the true change in the variance.\n",
"\n",
"We now compare these two models using [Pareto-smoothed importance sampling leave-one-out cross-validation](https://arxiv.org/abs/1507.04544) (PSIS-LOO)."
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "7263640f",
"metadata": {},
"outputs": [],
"source": [
"traces = {\n",
" 'Homoskedastic': trace,\n",
" 'Heteroskedastic': var_trace\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "61336cb2",
"metadata": {},
"outputs": [],
"source": [
"comp_df = az.compare(traces)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "3f3a68ee",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>rank</th>\n",
" <th>loo</th>\n",
" <th>p_loo</th>\n",
" <th>d_loo</th>\n",
" <th>weight</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Heteroskedastic</th>\n",
" <td>0</td>\n",
" <td>41.369658</td>\n",
" <td>17.759399</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Homoskedastic</th>\n",
" <td>1</td>\n",
" <td>-41.703944</td>\n",
" <td>14.188435</td>\n",
" <td>83.073602</td>\n",
" <td>8.058976e-11</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" rank loo p_loo d_loo weight\n",
"Heteroskedastic 0 41.369658 17.759399 0.000000 1.000000e+00\n",
"Homoskedastic 1 -41.703944 14.188435 83.073602 8.058976e-11"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"comp_df.loc[:, :\"weight\"]"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "80cd0b00",
"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()\n",
"\n",
"az.plot_compare(comp_df, plot_ic_diff=False, ax=ax);"
]
},
{
"cell_type": "markdown",
"id": "1305babf",
"metadata": {},
"source": [
"Interestingly, the PSIS-LOO score for the heteroskedastic model is significantly higher than that of the homoskedastic model, even though these two models predict essentially the same conditional mean.\n",
"\n",
"This post is available as a Jupyter notebook [here](https://nbviewer.jupyter.org/gist/AustinRochford/2b7a0f79457dc6b593309db433ecbedd)."
]
}
],
"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
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment