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@ColCarroll
Created Nov 30, 2019
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New features in PyMC3 v3.8
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PyMC3 v3.8\n",
"\n",
"Released 29 November, 2019\n",
"\n",
"See the full [release notes](https://github.com/pymc-devs/pymc3/blob/master/RELEASE-NOTES.md) here, but this highlights the new features on the list, in order.\n",
"\n",
"This is my own work, so apologies to the contributors for my failures in summing up their contributions, and please direct mistakes my way. Thanks also to all the contributors for the bug fixes, maintenance, code reviews, issue reporting, and so on that went into this release. I actually tried to *not* call out individual authors here, since open source is such a collaborative effort."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.8\n"
]
}
],
"source": [
"import pymc3 as pm\n",
"import numpy as np\n",
"from scipy.integrate import odeint\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"print(pm.__version__)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Implemented robust u turn check in NUTS (similar to [stan-dev/stan#2800](https://github.com/stan-dev/stan/pull/2800)) [#3605](https://github.com/pymc-devs/pymc3/pull/3605).\n",
"\n",
"This was a technical improvement on PyMC3's core algorithm, the No-U-Turn sampler (NUTS), probably best explained in the [Stan discourse page](https://discourse.mc-stan.org/t/nuts-misses-u-turns-runs-in-circles-until-max-treedepth/9727/15). \n",
"\n",
"Roughly, NUTS is distinguished from Hamiltonian Monte Carlo (HMC) in that it can explore posterior distributions of different scales using a dynamic path length. HMC, by contrast, will have a fixed path length. Longer paths will be slower, but produce \"more independent\" samples. NUTS uses a heuristic to balances these desires: when the trajectory \"makes a U-turn\", we stop integrating. \n",
"\n",
"User `nhuurre` found that this U-turn check was not actually catching all the U-turns, and the `Stan` development team was able to reproduce that this *could* and *did* actually occur, and that it was a technical, but not onerous, fix. End users do not need to do anything to opt into this feature (in fact, you *can't* opt out), but it is worth pointing out that this correction is implemented."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Add capabilities to do inference on parameters in a differential equation with `DifferentialEquation`. See [#3590](https://github.com/pymc-devs/pymc3/pull/3590) and [#3634](https://github.com/pymc-devs/pymc3/pull/3634).\n",
"\n",
"\n",
"This was completed as part of GSoC. See [Demetri's post](https://dpananos.github.io/posts/2019/08/blog-post-21/) on the work for a better description.\n",
"\n",
"Below is an example ODE, modelling an object in free fall under the effects of drag. We will try to estimate the drag coefficient under some uncertain observations."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [drag, sigma]\n",
"Sampling 4 chains, 0 divergences: 100%|██████████| 6000/6000 [01:58<00:00, 50.81draws/s]\n",
"100%|██████████| 2000/2000 [00:24<00:00, 81.56it/s]\n"
]
}
],
"source": [
"np.random.seed(0)\n",
"\n",
"def freefall(drag, t, velocity):\n",
" \"\"\"Equation for an object falling under the force of gravity.\n",
" \n",
" y' = mg - γy\n",
" \n",
" where y is velocity, m is the mass (we set to 1.), γ is drag, g is gravity (9.8 m/s^2).\n",
" \"\"\"\n",
" return 9.8 - velocity[0] * drag[0]\n",
"\n",
"\n",
"# Generate fake data\n",
"# Unobserved parameters are suffixed with \"_\", like \"drag_\"\n",
"times = np.arange(0, 10, 0.5)\n",
"drag_, sigma_ = 0.4, 2\n",
"y_ = odeint(freefall, t=times, y0=0., args=tuple([[drag_]]))\n",
"y_obs = np.random.normal(y_, sigma_)\n",
"\n",
"ode_model = pm.ode.DifferentialEquation(\n",
" func=freefall,\n",
" times=times,\n",
" n_states=1, \n",
" n_theta=1,\n",
" t0=0)\n",
"\n",
"with pm.Model():\n",
" sigma = pm.HalfCauchy('sigma', 1) \n",
" drag = pm.Lognormal('drag', 0, 1)\n",
" ode_solution = ode_model(y0=[0], theta=[drag])\n",
" Y = pm.Normal('Y', mu=ode_solution, sd=sigma, observed=y_obs)\n",
" \n",
" trace = pm.sample(500, tune=1000)\n",
" ppc = pm.sample_posterior_predictive(trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that the parameters for the drag and the observation noise were inferred, along with uncertainty estimates:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior for `sigma` and `drag` are calculated in the presence of noise, and we can plot the posterior predictive samples on top of the original dataset to see what might have happened if we reran the experiment using these posterior estimates:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/colin/miniconda3/envs/pymc33.7/lib/python3.7/site-packages/ipykernel_launcher.py:3: MatplotlibDeprecationWarning: cycling among columns of inputs with non-matching shapes is deprecated.\n",
" This is separate from the ipykernel package so we can avoid doing imports until\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(15, 4))\n",
"\n",
"ax.plot(np.tile(times[:, np.newaxis], 500), ppc['Y'].squeeze().T, 'k.', alpha=0.01)\n",
"ax.plot(times, y_, '-', label='True data')\n",
"ax.plot(times, y_obs, 'o', label='Observed data')\n",
"ax.set_xlabel('Time (s)')\n",
"ax.set_ylabel('Velocity (m/s)')\n",
"ax.set_xlim(left=0)\n",
"ax.set_ylim(bottom=0)\n",
"ax.set_title(f'Simulated data with drag={drag_} and noise={sigma_}')\n",
"\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Distinguish between `Data` and `Deterministic` variables when graphing models with graphviz. PR [#3491](https://github.com/pymc-devs/pymc3/pull/3491).\n",
"\n",
"This is a quality-of-life improvement on how the `model_to_graphviz` function draws a model. This PR added rounded corners to the `Data` node to distinguish it from a `Deterministic`, and also added an octagon for a `Potential` node."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Generated by graphviz version 2.42.3 (20191010.1750)\n",
" -->\n",
"<!-- Title: %3 Pages: 1 -->\n",
"<svg width=\"275pt\" height=\"299pt\"\n",
" viewBox=\"0.00 0.00 275.30 299.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 295)\">\n",
"<title>%3</title>\n",
"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-295 271.3,-295 271.3,4 -4,4\"/>\n",
"<g id=\"clust1\" class=\"cluster\">\n",
"<title>cluster3</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M93.5,-8C93.5,-8 243.5,-8 243.5,-8 249.5,-8 255.5,-14 255.5,-20 255.5,-20 255.5,-143 255.5,-143 255.5,-149 249.5,-155 243.5,-155 243.5,-155 93.5,-155 93.5,-155 87.5,-155 81.5,-149 81.5,-143 81.5,-143 81.5,-20 81.5,-20 81.5,-14 87.5,-8 93.5,-8\"/>\n",
"<text text-anchor=\"middle\" x=\"244\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\">3</text>\n",
"</g>\n",
"<!-- y -->\n",
"<g id=\"node1\" class=\"node\">\n",
"<title>y</title>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"113,-219 0,-219 0,-183 113,-183 113,-219\"/>\n",
"<text text-anchor=\"middle\" x=\"56.5\" y=\"-197.3\" font-family=\"Times,serif\" font-size=\"14.00\">y ~ Deterministic</text>\n",
"</g>\n",
"<!-- observed -->\n",
"<g id=\"node5\" class=\"node\">\n",
"<title>observed</title>\n",
"<ellipse fill=\"lightgrey\" stroke=\"black\" cx=\"168.5\" cy=\"-129\" rx=\"79.09\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"168.5\" y=\"-125.3\" font-family=\"Times,serif\" font-size=\"14.00\">observed ~ Normal</text>\n",
"</g>\n",
"<!-- y&#45;&gt;observed -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>y&#45;&gt;observed</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M83.9,-182.88C98.98,-173.45 117.84,-161.66 133.93,-151.61\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"135.91,-154.49 142.54,-146.23 132.2,-148.56 135.91,-154.49\"/>\n",
"</g>\n",
"<!-- x -->\n",
"<g id=\"node2\" class=\"node\">\n",
"<title>x</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"191.5\" cy=\"-273\" rx=\"51.99\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"191.5\" y=\"-269.3\" font-family=\"Times,serif\" font-size=\"14.00\">x ~ Normal</text>\n",
"</g>\n",
"<!-- x&#45;&gt;y -->\n",
"<g id=\"edge1\" class=\"edge\">\n",
"<title>x&#45;&gt;y</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M163.85,-257.67C145.04,-247.91 119.79,-234.82 98.5,-223.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"99.84,-220.53 89.35,-219.03 96.61,-226.74 99.84,-220.53\"/>\n",
"</g>\n",
"<!-- z -->\n",
"<g id=\"node3\" class=\"node\">\n",
"<title>z</title>\n",
"<polygon fill=\"none\" stroke=\"black\" points=\"252,-193.54 252,-208.46 216.56,-219 166.44,-219 131,-208.46 131,-193.54 166.44,-183 216.56,-183 252,-193.54\"/>\n",
"<text text-anchor=\"middle\" x=\"191.5\" y=\"-197.3\" font-family=\"Times,serif\" font-size=\"14.00\">z ~ Potential</text>\n",
"</g>\n",
"<!-- x&#45;&gt;z -->\n",
"<g id=\"edge2\" class=\"edge\">\n",
"<title>x&#45;&gt;z</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M191.5,-254.7C191.5,-246.98 191.5,-237.71 191.5,-229.11\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"195,-229.1 191.5,-219.1 188,-229.1 195,-229.1\"/>\n",
"</g>\n",
"<!-- x&#45;&gt;observed -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>x&#45;&gt;observed</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M221.07,-257.97C236.13,-249.1 253.02,-236.06 261.5,-219 268.62,-204.67 269.54,-196.83 261.5,-183 252.68,-167.82 237.71,-156.63 222.32,-148.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"223.78,-145.37 213.26,-144.14 220.72,-151.66 223.78,-145.37\"/>\n",
"</g>\n",
"<!-- my_observation -->\n",
"<g id=\"node4\" class=\"node\">\n",
"<title>my_observation</title>\n",
"<path fill=\"lightgrey\" stroke=\"black\" d=\"M229,-75C229,-75 108,-75 108,-75 102,-75 96,-69 96,-63 96,-63 96,-51 96,-51 96,-45 102,-39 108,-39 108,-39 229,-39 229,-39 235,-39 241,-45 241,-51 241,-51 241,-63 241,-63 241,-69 235,-75 229,-75\"/>\n",
"<text text-anchor=\"middle\" x=\"168.5\" y=\"-53.3\" font-family=\"Times,serif\" font-size=\"14.00\">my_observation ~ Data</text>\n",
"</g>\n",
"<!-- observed&#45;&gt;my_observation -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>observed&#45;&gt;my_observation</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M168.5,-110.7C168.5,-102.98 168.5,-93.71 168.5,-85.11\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"172,-85.1 168.5,-75.1 165,-85.1 172,-85.1\"/>\n",
"</g>\n",
"</g>\n",
"</svg>\n"
],
"text/plain": [
"<graphviz.dot.Digraph at 0x7f3dcaa969b0>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"with pm.Model() as model:\n",
" x = pm.Normal('x')\n",
" y = pm.Deterministic('y', np.abs(x))\n",
" pm.Potential('z', pm.Normal.dist().logp(x))\n",
" observation = pm.Data('my_observation', [1, 2, 0])\n",
" pm.Normal('observed', mu=x, sd=y, observed=observation)\n",
"\n",
"pm.model_to_graphviz(model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sequential Monte Carlo - Approximate Bayesian Computation step method is now available. The implementation is in an experimental stage and will be further improved.\n",
"\n",
"This is also known as likelihood-free inference. This provides a `Simulator` and a `sample_smc` method, and compares the simulated data with your observed data. Note also the warning when you use these functions!"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sample initial stage: ...\n",
"/home/colin/projects/pymc3/pymc3/smc/smc.py:120: UserWarning: Warning: SMC-ABC methods are experimental step methods and not yet recommended for use in PyMC3!\n",
" warnings.warn(EXPERIMENTAL_WARNING)\n",
"Stage: 0 Beta: 0.002 Steps: 25 Acce: 1.000\n",
"Stage: 1 Beta: 0.019 Steps: 25 Acce: 0.514\n",
"Stage: 2 Beta: 0.096 Steps: 6 Acce: 0.441\n",
"Stage: 3 Beta: 0.328 Steps: 7 Acce: 0.343\n",
"Stage: 4 Beta: 1.000 Steps: 10 Acce: 0.332\n",
"arviz.stats.stats_utils - WARNING - Shape validation failed: input_shape: (1, 1000), minimum_shape: (chains=2, draws=4)\n",
"arviz.stats.stats_utils - WARNING - Shape validation failed: input_shape: (1, 1000), minimum_shape: (chains=2, draws=4)\n"
]
},
{
"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>mean</th>\n",
" <th>sd</th>\n",
" <th>hpd_3%</th>\n",
" <th>hpd_97%</th>\n",
" <th>mcse_mean</th>\n",
" <th>mcse_sd</th>\n",
" <th>ess_mean</th>\n",
" <th>ess_sd</th>\n",
" <th>ess_bulk</th>\n",
" <th>ess_tail</th>\n",
" <th>r_hat</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>a</th>\n",
" <td>-0.017</td>\n",
" <td>0.114</td>\n",
" <td>-0.242</td>\n",
" <td>0.176</td>\n",
" <td>0.004</td>\n",
" <td>0.003</td>\n",
" <td>911.0</td>\n",
" <td>911.0</td>\n",
" <td>919.0</td>\n",
" <td>981.0</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>b</th>\n",
" <td>0.988</td>\n",
" <td>0.127</td>\n",
" <td>0.739</td>\n",
" <td>1.215</td>\n",
" <td>0.004</td>\n",
" <td>0.003</td>\n",
" <td>963.0</td>\n",
" <td>963.0</td>\n",
" <td>964.0</td>\n",
" <td>906.0</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" mean sd hpd_3% hpd_97% mcse_mean mcse_sd ess_mean ess_sd \\\n",
"a -0.017 0.114 -0.242 0.176 0.004 0.003 911.0 911.0 \n",
"b 0.988 0.127 0.739 1.215 0.004 0.003 963.0 963.0 \n",
"\n",
" ess_bulk ess_tail r_hat \n",
"a 919.0 981.0 NaN \n",
"b 964.0 906.0 NaN "
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = np.random.randn(1000)\n",
"\n",
"def normal_sim(a, b):\n",
" return np.sort(np.random.normal(a, b, 1000))\n",
"\n",
"\n",
"with pm.Model():\n",
" a = pm.Normal('a', mu=0, sd=5)\n",
" b = pm.HalfNormal('b', sd=1)\n",
" s = pm.Simulator('s', normal_sim, observed=np.sort(data))\n",
" trace_example = pm.sample_smc(kernel=\"ABC\", epsilon=0.1)\n",
"\n",
"pm.summary(trace_example)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Added `Matern12` covariance function for Gaussian processes. This is the Matern kernel with nu=1/2.\n",
"\n",
"The Matern kernels are parameterized by $\\nu$, and are generalizations of the radial basis function (RBF) kernel. They are computationally pleasant for $\\nu = \\infty$, which recovers the RBF kernel, $\\nu = 5/2$, which are twice differentiable functions, $\\nu = 3/2$, differentiable functions, and $\\nu = 1/2$, which is the absolute exponential kernel. PyMC3 already implemented `Matern52` and `Matern32`, so this completes the set. You can see comparisons below:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x720 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ls = 0.2\n",
"X = np.linspace(0, 2, 100)[:,None]\n",
"\n",
"fig, axes = plt.subplots(nrows=3, figsize=(15, 10), sharex=True, sharey=True)\n",
"\n",
"for name, ax in zip(('52', '32', '12'), axes.ravel()):\n",
" covariance = f'Matern{name}'\n",
" cov = getattr(pm.gp.cov, covariance)(1, ls)\n",
" K = cov(X).eval()\n",
"\n",
" ax.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T)\n",
" ax.set_title(covariance)\n",
" ax.set_ylabel(\"y\")\n",
" ax.set_xlabel(\"x\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Progressbar reports number of divergences in real time, when available [#3547](https://github.com/pymc-devs/pymc3/pull/3547).\n",
"\n",
"This is helpful for long running models: if you have tons of divergences, maybe you want to quit early and think about what you have done. Below is a model that most samplers have trouble with (Neal's funnel). This feature adds the `Sampling 4 chains, $N divergences` text."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [x, scale]\n",
"Sampling 4 chains, 5 divergences: 100%|██████████| 4000/4000 [00:05<00:00, 705.25draws/s] \n",
"There was 1 divergence after tuning. Increase `target_accept` or reparameterize.\n",
"The acceptance probability does not match the target. It is 0.5371405758649728, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"There was 1 divergence after tuning. Increase `target_accept` or reparameterize.\n",
"There were 3 divergences after tuning. Increase `target_accept` or reparameterize.\n",
"The acceptance probability does not match the target. It is 0.46186288892493643, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.\n",
"The estimated number of effective samples is smaller than 200 for some parameters.\n"
]
}
],
"source": [
"with pm.Model() as funnel:\n",
" scale = pm.Normal(\"scale\", mu=0, sd=3)\n",
" pm.Normal(\"x\", sd=pm.math.exp(scale / 2), shape=10)\n",
" trace = pm.sample()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sampling from variational approximation now allows for alternative trace backends [#3550](https://github.com/pymc-devs/pymc3/pull/3550).\n",
"\n",
"This is also something you can already do with inference, though alternative backends are not well supported (pull requests always welcome!), and now it works with variational inference as well."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Average Loss = 0.0024892: 100%|██████████| 10000/10000 [00:02<00:00, 3522.38it/s] \n",
"Finished [100%]: Average Loss = 0.0025052\n"
]
},
{
"data": {
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>draw</th>\n",
" <th>chain</th>\n",
" <th>v</th>\n",
" </tr>\n",
" <tr>\n",
" <th>recid</th>\n",
" <th></th>\n",
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" <tr>\n",
" <th>4</th>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>-1.458609</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>4</td>\n",
" <td>0</td>\n",
" <td>0.977264</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" draw chain v\n",
"recid \n",
"1 0 0 0.249017\n",
"2 1 0 -2.217926\n",
"3 2 0 -0.489882\n",
"4 3 0 -1.458609\n",
"5 4 0 0.977264"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"import sqlite3\n",
"\n",
"with pm.Model():\n",
" pm.Normal('x')\n",
" \n",
" fit = pm.fit()\n",
" trace = fit.sample(backend='sqlite', name='trace.db')\n",
"\n",
"db = sqlite3.connect('trace.db')\n",
"pd.read_sql('SELECT * FROM x', db, index_col='recid').head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Infix `@` operator now works with random variables and deterministics [#3619](https://github.com/pymc-devs/pymc3/pull/3619).\n",
"\n",
"Another quality of life improvement. To use the matrix multiplication operator that has been available since Python 3.5."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"X = np.random.randn(100, 1)\n",
"w = np.random.randn(1)\n",
"y = X @ w + (np.random.randn(100) * .1)\n",
"\n",
"with pm.Model() as linear_model:\n",
" weights = pm.Normal('weights', mu=0, sigma=1)\n",
" noise = pm.Gamma('noise', alpha=2, beta=1)\n",
" y_observed = pm.Normal('y_observed',\n",
" mu=X @ weights,\n",
" sigma=noise,\n",
" observed=y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [ArviZ](https://arviz-devs.github.io/arviz/) is now a requirement, and handles plotting, diagnostics, and statistical checks.\n",
"\n",
"Check out [the ArviZ docs](https://arviz-devs.github.io/arviz/), and file issues as they come up. This transition might be at least a little bumpy, but it unifies efforts between a number of different probabilistic programming libraries, and makes sure that calculations like effective sample size are consistent between these different libraries."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Can use GaussianRandomWalk in `sample_prior_predictive` and `sample_prior_predictive` [#3682](https://github.com/pymc-devs/pymc3/pull/3682).\n",
"\n",
"There has been considerable work over the past year in allowing prior predictive and posterior predictive sampling, and this starts implementing these methods for the `GaussianRandomWalk`. This allowed the [stochastic volatility example](https://docs.pymc.io/notebooks/stochastic_volatility.html) to be rewritten and including a prior- and posterior-predictive check.\n",
"\n",
"Here we are just using the `.random()` method directly to generate 3 series of length 1,000:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1008x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(14, 4))\n",
"ax.plot(pm.GaussianRandomWalk.dist(shape=(1000, 3)).random());"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Now 11 years of S&P returns in data set [#3682](https://github.com/pymc-devs/pymc3/pull/3682).\n",
"Again in service of the [stochastic volatility example](https://docs.pymc.io/notebooks/stochastic_volatility.html), PyMC3 ships with 11 years of data!"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"returns = pd.read_csv(pm.get_data(\"SP500.csv\"), index_col='Date')\n",
"returns[\"change\"] = np.log(returns[\"Close\"]).diff()\n",
"returns = returns.dropna()\n",
"\n",
"fig, ax = plt.subplots(figsize=(14, 4))\n",
"returns.plot(y=\"change\", label='S&P 500', ax=ax)\n",
"ax.set(xlabel='time', ylabel='returns')\n",
"ax.legend();"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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