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‎README.rst

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- `Probabilistic Programming and Bayesian Methods for Hackers <https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers>`__: Fantastic book with many applied code examples.
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- `PyMC3 port of the book "Doing Bayesian Data Analysis" by John Kruschke <https://github.com/aloctavodia/Doing_bayesian_data_analysis>`__ as well as the `second edition <https://github.com/JWarmenhoven/DBDA-python>`__: Principled introduction to Bayesian data analysis.
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- `PyMC3 port of the book "Statistical Rethinking A Bayesian Course with Examples in R and Stan" by Richard McElreath <https://github.com/aloctavodia/Statistical-Rethinking-with-Python-and-PyMC3>`__
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- `PyMC3 port of the book "Bayesian Cognitive Modeling" by Michael Lee and EJ Wagenmakers <https://github.com/junpenglao/Bayesian-Cognitive-Modeling-in-Pymc3>`__: Focused on using Bayesian statistics in cognitive modeling.
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- `PyMC3 port of the book "Statistical Rethinking A Bayesian Course with Examples in R and Stan" by Richard McElreath <https://github.com/pymc-devs/resources/tree/master/Rethinking>`__
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- `PyMC3 port of the book "Bayesian Cognitive Modeling" by Michael Lee and EJ Wagenmakers <https://github.com/pymc-devs/resources/tree/master/BCM>`__: Focused on using Bayesian statistics in cognitive modeling.
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- `Bayesian Analysis with Python by Osvaldo Martin <https://www.packtpub.com/big-data-and-business-intelligence/bayesian-analysis-python>`__ (and `errata <https://github.com/aloctavodia/BAP>`__): Great introductory book.
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PyMC3 talks

‎RELEASE-NOTES.md

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- Renamed `sample_ppc()` and `sample_ppc_w()` to `sample_posterior_predictive()` and `sample_posterior_predictive_w()`, respectively.
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- Refactor SMC and properly compute marginal likelihood (#3124)
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## PyMC 3.5 (July 21 2018)
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### New features

‎build_and_deploy_docs.sh

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#!/bin/sh
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latesttag=$(git describe --tags `git rev-list --tags --max-count=1`)
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echo checking out ${latesttag}
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git checkout ${latesttag}
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pushd docs/source
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make html
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ghp-import -c docs.pymc.io -n -p _build/html/

‎docs/source/advanced_theano.rst

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# fit the model
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trace = pm.sample()
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# Switch out the observations and use `sample_ppc` to predict
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# Switch out the observations and use `sample_posterior_predictive` to predict
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x_shared.set_value([-1, 0, 1.])
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post_pred = pm.sample_ppc(trace, samples=500)
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post_pred = pm.sample_posterior_predictive(trace, samples=500)
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However, due to the way we handle shapes at the moment, it is
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not possible to change the shape of a shared variable if that would

‎docs/source/examples.rst

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notebooks/PyMC3_tips_and_heuristic.ipynb
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notebooks/LKJ.ipynb
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notebooks/live_sample_plots.ipynb
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notebooks/sampling_compound_step.ipynb
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Applied
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=======

‎docs/source/intro.rst

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Purpose
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=======
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PyMC3 is a probabilistic programming module for Python that allows users to fit Bayesian models using a variety of numerical methods, most notably Markov chain Monte Carlo (MCMC) and variational inference (VI). Its flexibility and extensibility make it applicable to a large suite of problems. Along with core model specification and fitting functionality, PyMC3 includes functionality for summarizing output and for model diagnostics.
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PyMC3 is a probabilistic programming package for Python that allows users to fit Bayesian models using a variety of numerical methods, most notably Markov chain Monte Carlo (MCMC) and variational inference (VI). Its flexibility and extensibility make it applicable to a large suite of problems. Along with core model specification and fitting functionality, PyMC3 includes functionality for summarizing output and for model diagnostics.
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‎docs/source/notebooks/Bayes_factor.ipynb

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],
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"source": [
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"_, ax = plt.subplots()\n",
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"ppc_0 = pm.sample_ppc(traces[0], 1000, models[0], size=(len(y), 20))\n",
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"ppc_1 = pm.sample_ppc(traces[1], 1000, models[1], size=(len(y), 20))\n",
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"ppc_0 = pm.sample_posterior_predictive(traces[0], 1000, models[0], size=(len(y), 20))\n",
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"ppc_1 = pm.sample_posterior_predictive(traces[1], 1000, models[1], size=(len(y), 20))\n",
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"for m_0, m_1 in zip(ppc_0['yl'].T, ppc_1['yl'].T):\n",
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" pm.kdeplot(np.mean(m_0, 0), ax=ax, color='C0', label='model 0')\n",
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" pm.kdeplot(np.mean(m_1, 0), ax=ax, color='C1', label='model 1')\n",

‎docs/source/notebooks/Euler-Maruyama and SDEs.ipynb renamed to ‎docs/source/notebooks/Euler-Maruyama_and_SDEs.ipynb

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],
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"source": [
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"# generate trace from posterior\n",
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"ppc_trace = pm.sample_ppc(trace, model=model)\n",
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"ppc_trace = pm.sample_posterior_predictive(trace, model=model)\n",
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"\n",
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"# plot with data\n",
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"figure(figsize=(10, 3))\n",
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],
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"source": [
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"# generate trace from posterior\n",
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"ppc_trace = pm.sample_ppc(trace, model=model)\n",
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"ppc_trace = pm.sample_posterior_predictive(trace, model=model)\n",
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"\n",
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"# plot with data\n",
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"figure(figsize=(10, 3))\n",

‎docs/source/notebooks/GLM-robust-with-outlier-detection.ipynb

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‎docs/source/notebooks/GP-Latent.ipynb

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"\n",
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"### Using `.conditional`\n",
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"\n",
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"Next, we extend the model by adding the conditional distribution so we can predict at new $x$ locations. Lets see how the extrapolation looks out to higher $x$. To do this, we extend our `model` with the `conditional` distribution of the GP. Then, we can sample from it using the `trace` and the `sample_ppc` function. This is similar to how Stan uses its `generated quantities {...}` blocks. We could have included `gp.conditional` in the model *before* we did the NUTS sampling, but it is more efficient to separate these steps."
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"Next, we extend the model by adding the conditional distribution so we can predict at new $x$ locations. Lets see how the extrapolation looks out to higher $x$. To do this, we extend our `model` with the `conditional` distribution of the GP. Then, we can sample from it using the `trace` and the `sample_posterior_predictive` function. This is similar to how Stan uses its `generated quantities {...}` blocks. We could have included `gp.conditional` in the model *before* we did the NUTS sampling, but it is more efficient to separate these steps."
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]
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},
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{
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"\n",
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"# Sample from the GP conditional distribution\n",
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"with model:\n",
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" pred_samples = pm.sample_ppc(trace, vars=[f_pred], samples=1000)"
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" pred_samples = pm.sample_posterior_predictive(trace, vars=[f_pred], samples=1000)"
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]
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},
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{
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" f_pred = gp.conditional(\"f_pred\", X_new)\n",
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"\n",
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"with model:\n",
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" pred_samples = pm.sample_ppc(trace, vars=[f_pred], samples=1000)"
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" pred_samples = pm.sample_posterior_predictive(trace, vars=[f_pred], samples=1000)"
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]
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},
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{

‎docs/source/notebooks/GP-Marginal.ipynb

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"\n",
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"# To use the MAP values, you can just replace the trace with a length-1 list with `mp`\n",
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"with model:\n",
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" pred_samples = pm.sample_ppc([mp], vars=[f_pred], samples=2000)"
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" pred_samples = pm.sample_posterior_predictive([mp], vars=[f_pred], samples=2000)"
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]
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},
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{
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"source": [
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"with model:\n",
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" y_pred = gp.conditional(\"y_pred\", X_new, pred_noise=True)\n",
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" y_samples = pm.sample_ppc([mp], vars=[y_pred], samples=2000)"
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" y_samples = pm.sample_posterior_predictive([mp], vars=[y_pred], samples=2000)"
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]
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},
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{

‎docs/source/notebooks/GP-SparseApprox.ipynb

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"\n",
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"# To use the MAP values, you can just replace the trace with a length-1 list with `mp`\n",
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"with model:\n",
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" pred_samples = pm.sample_ppc(trace, vars=[f_pred], samples=1000)"
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" pred_samples = pm.sample_posterior_predictive(trace, vars=[f_pred], samples=1000)"
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]
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{

‎docs/source/notebooks/GP-TProcess.ipynb

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"\n",
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"# Sample from the GP conditional distribution\n",
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"with model:\n",
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" pred_samples = pm.sample_ppc(tr, vars=[f_pred], samples=1000)"
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" pred_samples = pm.sample_posterior_predictive(tr, vars=[f_pred], samples=1000)"
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]
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},
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{

‎docs/source/notebooks/api_quickstart.ipynb

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"source": [
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"## 4. Posterior Predictive Sampling\n",
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"\n",
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"The `sample_ppc()` function performs prediction on hold-out data and posterior predictive checks."
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"The `sample_posterior_predictive()` function performs prediction on hold-out data and posterior predictive checks."
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]
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],
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"source": [
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"with model:\n",
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" post_pred = pm.sample_ppc(trace, samples=500, size=len(data))"
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" post_pred = pm.sample_posterior_predictive(trace, samples=500, size=len(data))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"`sample_ppc()` returns a dict with a key for every observed node:"
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"`sample_posterior_predictive()` returns a dict with a key for every observed node:"
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]
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{
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"y_shared.set_value([0, 0, 0]) # dummy values\n",
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"\n",
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"with model:\n",
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" post_pred = pm.sample_ppc(trace, samples=500)"
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" post_pred = pm.sample_posterior_predictive(trace, samples=500)"
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]
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{

‎docs/source/notebooks/bayes_param_survival_pymc3.ipynb

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],
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"source": [
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"with weibull_model:\n",
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" pp_weibull_trace = pm.sample_ppc(\n",
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" pp_weibull_trace = pm.sample_posterior_predictive(\n",
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" weibull_trace, samples=1500, vars=[y_obs]\n",
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" )"
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"cens_.set_value(cens_pp)\n",
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"\n",
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"with log_logistic_model:\n",
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" pp_log_logistic_trace = pm.sample_ppc(\n",
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" pp_log_logistic_trace = pm.sample_posterior_predictive(\n",
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" log_logistic_trace, samples=1500, vars=[y_obs]\n",
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" )"
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‎docs/source/notebooks/bayesian_neural_network_advi.ipynb

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"source": [
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"Now that we trained our model, lets predict on the hold-out set using a posterior predictive check (PPC). \n",
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"\n",
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"1. We can use [`sample_ppc()`](../api/inference.rst) to generate new data (in this case class predictions) from the posterior (sampled from the variational estimation).\n",
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"1. We can use [`sample_posterior_predictive()`](../api/inference.rst) to generate new data (in this case class predictions) from the posterior (sampled from the variational estimation).\n",
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"2. It is better to get the node directly and build theano graph using our approximation (`approx.sample_node`) , we get a lot of speed up"
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" ann_input.set_value(X_test)\n",
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" ann_output.set_value(Y_test)\n",
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" with neural_network:\n",
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" ppc = pm.sample_ppc(trace, samples=500, progressbar=False)\n",
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" ppc = pm.sample_posterior_predictive(trace, samples=500, progressbar=False)\n",
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"\n",
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" # Use probability of > 0.5 to assume prediction of class 1\n",
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" pred = ppc['out'].mean(axis=0) > 0.5\n",

‎docs/source/notebooks/bayesian_neural_network_with_sgfs.ipynb

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"ann_output.set_value(Y_test)\n",
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"\n",
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"# Creater posterior predictive samples\n",
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"ppc = pm.sample_ppc(trace, model=neural_network, samples=500, random_seed=0)\n",
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"ppc = pm.sample_posterior_predictive(trace, model=neural_network, samples=500, random_seed=0)\n",
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"\n",
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"# Use probability of > 0.5 to assume prediction of class 1\n",
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"pred = ppc['out'].mean(axis=0) > 0.5"
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"ann_output.set_value(dummy_out)\n",
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"\n",
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"# Creater posterior predictive samples\n",
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"ppc = pm.sample_ppc(trace, model=neural_network, samples=500, random_seed=0)"
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"ppc = pm.sample_posterior_predictive(trace, model=neural_network, samples=500, random_seed=0)"
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‎docs/source/notebooks/constant_stochastic_gradient.ipynb

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"samples = 1000\n",
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"\n",
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"# Creater posterior predictive samples\n",
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"sgfs_ppc = pm.sample_ppc(sgfs_trace, model=model, samples=samples, random_seed=0)\n",
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"sgfs_ppc = pm.sample_posterior_predictive(sgfs_trace, model=model, samples=samples, random_seed=0)\n",
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"sgfs_pred = sgfs_ppc['y_obs'].mean(axis=0)\n",
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"\n",
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"# Creater posterior predictive samples\n",
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"csg_ppc = pm.sample_ppc(csg_trace, model=model, samples=samples, random_seed=0)\n",
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"csg_ppc = pm.sample_posterior_predictive(csg_trace, model=model, samples=samples, random_seed=0)\n",
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"csg_pred = csg_ppc['y_obs'].mean(axis=0)\n",
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"\n",
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"# Nuts predictive samples\n",
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"nuts_ppc = pm.sample_ppc(nuts_trace, model=model, samples=samples, random_seed=0)\n",
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"nuts_ppc = pm.sample_posterior_predictive(nuts_trace, model=model, samples=samples, random_seed=0)\n",
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"nuts_pred = nuts_ppc['y_obs'].mean(axis=0)\n",
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"\n",
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"sgfs_diff = sgfs_pred-test_Y\n",

‎docs/source/notebooks/dependent_density_regression.ipynb

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"x_lidar.set_value(lidar_pp_x[:, np.newaxis])\n",
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"\n",
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"with model:\n",
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" pp_trace = pm.sample_ppc(trace, PP_SAMPLES, random_seed=SEED)"
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" pp_trace = pm.sample_posterior_predictive(trace, PP_SAMPLES, random_seed=SEED)"
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]
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{

‎docs/source/notebooks/marginalized_gaussian_mixture_model.ipynb

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],
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"with model:\n",
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" ppc_trace = pm.sample_ppc(trace, 5000, random_seed=SEED)"
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" ppc_trace = pm.sample_posterior_predictive(trace, 5000, random_seed=SEED)"
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‎docs/source/notebooks/model_averaging.ipynb

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"\n",
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"We can also see that we get a column with the relative `weight` for each model (according to the first equation at the beginning of this notebook). This weights can be _vaguely_ interpreted as the probability that each model will make the correct predictions on future data. Of course this interpretation is conditional on the models used to compute the weights, if we add or remove models the weights will change. And also is dependent on the assumptions behind WAIC (or any other Information Criterion used). So try to do not overinterpret these `weights`. \n",
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"\n",
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"Now we are going to use copmuted `weights` to generate predictions based not on a single model but on the weighted set of models. This is one way to perform model averaging. Using PyMC3 we can call the `sample_ppc_w` function as follows:"
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"Now we are going to use copmuted `weights` to generate predictions based not on a single model but on the weighted set of models. This is one way to perform model averaging. Using PyMC3 we can call the `sample_posterior_predictive_w` function as follows:"
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]
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},
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{
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},
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"outputs": [],
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"source": [
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"ppc_w = pm.sample_ppc_w(traces, 1000, models,\n",
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"ppc_w = pm.sample_posterior_predictive_w(traces, 1000, models,\n",
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" weights=comp.weight.sort_index(ascending=True),\n",
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" progressbar=False)"
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},
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"outputs": [],
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"source": [
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"ppc_2 = pm.sample_ppc(trace_2, 1000, model_2,\n",
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"ppc_2 = pm.sample_posterior_predictive(trace_2, 1000, model_2,\n",
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‎docs/source/notebooks/multilevel_modeling.ipynb

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"\n",
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"Radon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n",
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"\n",
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"![radon](http://www.fix-your-radon.com/images/how_radon_enters.jpg)\n",
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"![radon](https://www.cgenarchive.org/uploads/2/5/2/6/25269392/7758459_orig.jpg)\n",
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‎docs/source/notebooks/posterior_predictive.ipynb

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}
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],
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"source": [
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"ppc = pm.sample_posterior_predictive(trace, samples=500, model=model)"
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],
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"source": [
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"# Simply running PPC will use the updated values and do prediction\n",
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"ppc = pm.sample_ppc(trace, model=model, samples=100)"
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"ppc = pm.sample_posterior_predictive(trace, model=model, samples=100)"
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{
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"source": [
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"### Mean predicted values plus error bars to give sense of uncertainty in prediction\n",
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"\n",
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"Note that these are uncertainty caused by MCMC estimation, and not from the underlying model. If we had taken more samples in `sample_ppc`, the error bars would get smaller quite quickly."
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"Note that these are uncertainty caused by MCMC estimation, and not from the underlying model. If we had taken more samples in `sample_posterior_predictive`, the error bars would get smaller quite quickly."
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‎docs/source/notebooks/rugby_analytics.ipynb

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],
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" pp_trace = pm.sample_posterior_predictive(trace)"
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{

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