Sampling functions#

Expand for references to pymc.sample

Estimating parameters of a distribution from awkwardly binned data / Example 4: Parameter estimation with continuous and binned measures / Model Specification

Estimating parameters of a distribution from awkwardly binned data / Example 5: Hierarchical estimation / Model specification

Estimating parameters of a distribution from awkwardly binned data / Example 1: Gaussian parameter estimation with one set of bins / Model specification

Factor analysis / Model / Alternative parametrization

Factor analysis / Model / Direct implementation

Hierarchical Partial Pooling / Approach

NBA Foul Analysis with Item Response Theory / Sampling and convergence

Probabilistic Matrix Factorization for Making Personalized Recommendations / Probabilistic Matrix Factorization

Model building and expansion for golf putting / A new model

Model building and expansion for golf putting / Fitting the distance angle model

Model building and expansion for golf putting / Fitting the model on the new data

Model building and expansion for golf putting / Logit model

Model building and expansion for golf putting / Geometry-based model / Prior Predictive Checks

Fitting a Reinforcement Learning Model to Behavioral Data with PyMC / Estimating the learning parameters via PyMC / Alternative model using Bernoulli for the likelihood

Fitting a Reinforcement Learning Model to Behavioral Data with PyMC / Estimating the learning parameters via PyMC

Reliability Statistics and Predictive Calibration / Bayesian Modelling of Reliability Data / Direct PYMC implementation of Weibull Survival

A Hierarchical model for Rugby prediction / Building of the model

Introduction to Bayesian A/B Testing / Bernoulli Conversions / Data

Introduction to Bayesian A/B Testing / Generalising to multi-variant tests

Introduction to Bayesian A/B Testing / Value Conversions

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Double/Debiased Machine Learning and Frisch-Waugh-Lovell / Applying Debiased ML Methods

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Mediation Effects and Causal Structure

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Non-Confounded Inference: NHEFS Data / Propensity Score Modelling

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Non-Confounded Inference: NHEFS Data / Regression with Propensity Scores

Difference in differences / Bayesian difference in differences / Inference

Counterfactual inference: calculating excess deaths due to COVID-19 / Inference

Interrupted time series analysis / Inference

Bayesian mediation analysis / Define the PyMC model and conduct inference

Bayesian mediation analysis / Double check with total effect only model

Does the effect of training upon muscularity decrease with age? / Define the PyMC model and conduct inference

Regression discontinuity design analysis / Inference

Bayes Factors and Marginal Likelihood / Savage-Dickey Density Ratio

Model Averaging / Weighted posterior predictive samples

Sampler Statistics / Multiple samplers

Sampler Statistics

Using Data Containers / Applied example: height of toddlers as a function of age

Using Data Containers / Applied Example: Using Data containers as input to a binomial GLM

Using Data Containers / Using Data Containers for readability and reproducibility / Named dimensions with data containers

Using Data Containers / Using Data Containers to mutate data / Using Data container variables to fit the same model to several datasets

Using Data Containers / Using Data Containers for readability and reproducibility

Baby Births Modelling with HSGPs / EDA and Feature Engineering / Model Fitting and Diagnostics

Kronecker Structured Covariances / LatentKron / Model

Gaussian Processes: Latent Variable Implementation / Example 1: Regression with Student-T distributed noise / Coding the model in PyMC

Gaussian Processes: Latent Variable Implementation / Example 2: Classification

Marginal Likelihood Implementation / Example: Regression with white, Gaussian noise

Example 1: A hierarchical HSGP, a more custom model / Example 2: An HSGP that exploits Kronecker structure / Sampling & Convergence checks

Example 1: A hierarchical HSGP, a more custom model / Looking for a beginner’s introduction? / Sampling & Convergence checks

Gaussian Processes: HSGP Reference & First Steps / Example 1: Basic HSGP Usage / Define and fit the HSGP model

Gaussian Processes: HSGP Reference & First Steps / Example 1: Basic HSGP Usage / Example 2: Working with HSGPs as a parametric, linear model / Results

Inference

Binomial regression / Binomial regression model

Discrete Choice and Random Utility Models / Choosing Crackers over Repeated Choices: Mixed Logit Model

Discrete Choice and Random Utility Models / Experimental Model: Adding Correlation Structure

Discrete Choice and Random Utility Models / Improved Model: Adding Alternative Specific Intercepts

Discrete Choice and Random Utility Models / The Basic Model

Hierarchical Binomial Model: Rat Tumor Example / Computing the Posterior using PyMC

GLM: Negative Binomial Regression / Negative Binomial Regression / Create GLM Model

Ordinal Scales and Survey Data / Fit a variety of Model Specifications / Bayesian Particularities

Ordinal Scales and Survey Data / Liddell and Kruschke’s IMDB movie Ratings Data

Out-Of-Sample Predictions / Define and Fit the Model

GLM: Poisson Regression / Poisson Regression / 1. Manual method, create design matrices and manually specify model

Setup / 5. Linear Model with Custom Likelihood to Distinguish Outliers: Hogg Method / 5.2 Fit Model / 5.2.1 Sample Posterior

Setup / 4. Simple Linear Model with Robust Student-T Likelihood / 4.2 Fit Model / 4.2.1 Sample Posterior

Setup / 3. Simple Linear Model with no Outlier Correction / 3.2 Fit Model / 3.2.1 Sample Posterior

GLM: Robust Linear Regression / Robust Regression / Normal Likelihood

Rolling Regression / Rolling regression

Rolling Regression

Simpson’s paradox and mixed models / Model 1: Basic linear regression / Do inference

Simpson’s paradox and mixed models / Model 2: Independent slopes and intercepts model

Simpson’s paradox and mixed models / Model 3: Hierarchical regression

Bayesian regression with truncated or censored data / Run the truncated and censored regressions

Bayesian regression with truncated or censored data / The problem that truncated or censored regression solves

A Primer on Bayesian Methods for Multilevel Modeling / Adding group-level predictors

A Primer on Bayesian Methods for Multilevel Modeling / Conventional approaches

A Primer on Bayesian Methods for Multilevel Modeling / Adding group-level predictors / Correlations among levels

A Primer on Bayesian Methods for Multilevel Modeling / Non-centered Parameterization

A Primer on Bayesian Methods for Multilevel Modeling / Partial pooling model

A Primer on Bayesian Methods for Multilevel Modeling / Varying intercept and slope model

A Primer on Bayesian Methods for Multilevel Modeling / Varying intercept model

LKJ Cholesky Covariance Priors for Multivariate Normal Models

Bayesian Missing Data Imputation / Bayesian Imputation

Bayesian Missing Data Imputation / Bayesian Imputation by Chained Equations / PyMC Imputation

Using a “black box” likelihood function / Comparison to equivalent PyMC distributions

Using a “black box” likelihood function / PyTensor Op with gradients / Model definition

Using a “black box” likelihood function / Introduction

Using a “black box” likelihood function / PyTensor Op without gradients / Model definition

Using a “black box” likelihood function / Using a Potential instead of CustomDist

Bayesian copula estimation: Describing correlated joint distributions / PyMC models for copula and marginal estimation

How to debug a model / Introduction / Bringing it all together

How to debug a model / Introduction / Troubleshooting a toy PyMC model

Automatic marginalization of discrete variables / Coal mining model

Automatic marginalization of discrete variables / Gaussian Mixture model

Using ModelBuilder class for deploying PyMC models / Standard syntax

Splines / The model / Fit the model

Updating Priors / Words of Caution / Model specification

How to wrap a JAX function for use in PyMC / Wrapping the JAX function in PyTensor / Sampling with PyMC

General API quickstart / 3. Inference / 3.2 Analyze sampling results

General API quickstart / 4. Posterior Predictive Sampling

General API quickstart / 4.1 Predicting on hold-out data

General API quickstart / 3. Inference / 3.1 Sampling

Dirichlet mixtures of multinomials / Dirichlet-Multinomial Model - Explicit Mixture

Dirichlet mixtures of multinomials / Dirichlet-Multinomial Model - Marginalized

Dirichlet mixtures of multinomials / Multinomial model

Dirichlet process mixtures for density estimation / Dirichlet process mixtures

Gaussian Mixture Model

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways / Gradient-Free Sampler Options / DE MetropolisZ Sampler

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways / Gradient-Free Sampler Options / DEMetropolis Sampler

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways / Bayesian Inference with Gradients / Simulate with Pytensor Scan / Inference Using NUTs

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways / Bayesian Inference with Gradients / PyMC ODE Module / Inference with NUTS

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways / Gradient-Free Sampler Options / Metropolis Sampler

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways / Gradient-Free Sampler Options / Slice Sampler

DEMetropolis and DEMetropolis(Z) Algorithm Comparisons / Helper Functions / Sampling

DEMetropolis(Z) Sampler Tuning / Conclusions

DEMetropolis(Z) Sampler Tuning / Helper Functions / Sampling

Work flow / Step 4: Draw MCMC samples from the posterior using MLDA

Lasso regression with block updating

Compound Steps in Sampling / Compound steps

Compound Steps in Sampling / Compound steps by default

Compound Steps in Sampling / Order of step methods

Compound Steps in Sampling / Specify compound steps

Conditional Autoregressive (CAR) model / Writing some models in PyMC / Our first model: an independent random effects model

Conditional Autoregressive (CAR) model / Writing some models in PyMC / Our second model: a spatial random effects model (with fixed spatial dependence)

Conditional Autoregressive (CAR) model / Writing some models in PyMC / Our third model: a spatial random effects model, with unknown spatial dependence

Demonstrating the BYM model on the New York City pedestrian accidents dataset / Sampling the model

Censored Data Models / Censored data models / Model 1 - Imputed Censored Model of Censored Data

Censored Data Models / Censored data models / Model 2 - Unimputed Censored Model of Censored Data

Censored Data Models / Uncensored Model

Frailty and Survival Regression Models / Accelerated Failure Time Models

Frailty and Survival Regression Models / Fit Basic Cox Model with Fixed Effects

Frailty and Survival Regression Models / Fit Model with Shared Frailty terms by Individual

Bayesian Survival Analysis / Bayesian proportional hazards model

Bayesian Survival Analysis / Bayesian proportional hazards model / Time varying effects

Reparameterizing the Weibull Accelerated Failure Time Model / Parameterization 1

Reparameterizing the Weibull Accelerated Failure Time Model / Parameterization 2

Reparameterizing the Weibull Accelerated Failure Time Model / Parameterization 3

Analysis of An AR(1) Model in PyMC

Analysis of An AR(1) Model in PyMC / Extension to AR(p)

Air passengers - Prophet-like model / Part 1: linear trend

Air passengers - Prophet-like model / Part 2: enter seasonality

Forecasting with Structural AR Timeseries / Complicating the Picture / Specifying a Trend Model

Forecasting with Structural AR Timeseries / Specifying the Model

Forecasting with Structural AR Timeseries / Complicating the picture further / Specifying the Trend + Seasonal Model

Forecasting with Structural AR Timeseries / Complicating the Picture / Wrapping our model into a function

Multivariate Gaussian Random Walk / Model

Time Series Models Derived From a Generative Graph / Motivation / Define AR(2) Process / Posterior

Bayesian Vector Autoregressive Models / Handling Multiple Lags and Different Dimensions

Non-Linear Change Trajectories / A Minimal Model

Non-Linear Change Trajectories / Adding in Polynomial Time

Non-Linear Change Trajectories / Behaviour over time

Non-Linear Change Trajectories / Comparing Trajectories across Gender

Modelling Change over Time. / Model controlling for Peer Effects

Modelling Change over Time. / The Unconditional Mean Model

Modelling Change over Time. / The Uncontrolled Effects of Parental Alcoholism

Modelling Change over Time. / Unconditional Growth Model

Stochastic Volatility model / Fit Model

GLM: Mini-batch ADVI on hierarchical regression model

Empirical Approximation overview / 2d density

Empirical Approximation overview / Multimodal density

Introduction to Variational Inference with PyMC / Basic setup

Introduction to Variational Inference with PyMC / Distributional Approximations

Expand for references to pymc.sample_posterior_predictive

Categorical regression / Fitting independent trees

Categorical regression / Model Specification

Modeling Heteroscedasticity with BART / Model Specification

Bayesian Additive Regression Trees: Introduction / Biking with BART / Out-of-Sample Predictions / Regression

Bayesian Additive Regression Trees: Introduction / Biking with BART / Out-of-Sample Predictions / Time Series

Quantile Regression with BART / Asymmetric Laplace distribution

Estimating parameters of a distribution from awkwardly binned data / Example 1: Gaussian parameter estimation with one set of bins / Checks on model

Estimating parameters of a distribution from awkwardly binned data / Example 5: Hierarchical estimation / Posterior predictive checks

Estimating parameters of a distribution from awkwardly binned data / Example 6: A non-normal distribution / Posterior predictive checks

Estimating parameters of a distribution from awkwardly binned data / Example 3: Parameter estimation with two bins together / Posterior predictive checks

Estimating parameters of a distribution from awkwardly binned data / Example 4: Parameter estimation with continuous and binned measures / Posterior predictive checks

Estimating parameters of a distribution from awkwardly binned data / Example 2: Parameter estimation with the other set of bins / Posterior predictive checks

Model building and expansion for golf putting / A new model

Model building and expansion for golf putting / Fitting the distance angle model

Model building and expansion for golf putting / Logit model

Reliability Statistics and Predictive Calibration / Bayesian Modelling of Reliability Data / Direct PYMC implementation of Weibull Survival

A Hierarchical model for Rugby prediction / Results

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Double/Debiased Machine Learning and Frisch-Waugh-Lovell / Applying Debiased ML Methods

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Non-Confounded Inference: NHEFS Data / Causal Inference as Regression Imputation

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Mediation Effects and Causal Structure / Mediation Estimands

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Non-Confounded Inference: NHEFS Data / Propensity Score Modelling

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Non-Confounded Inference: NHEFS Data / Regression with Propensity Scores

Difference in differences / Bayesian difference in differences / Posterior prediction

Counterfactual inference: calculating excess deaths due to COVID-19 / Counterfactual inference

Counterfactual inference: calculating excess deaths due to COVID-19 / Posterior predictive check

Interrupted time series analysis / Counterfactual inference

Interrupted time series analysis / Posterior predictive check

Regression discontinuity design analysis / Counterfactual questions

Bayes Factors and Marginal Likelihood / Bayes factors and inference

Model Averaging / Weighted posterior predictive samples

Using Data Containers / Applied example: height of toddlers as a function of age

Using Data Containers / Applied Example: Using Data containers as input to a binomial GLM

Baby Births Modelling with HSGPs / EDA and Feature Engineering / Model Fitting and Diagnostics

Kronecker Structured Covariances / LatentKron / Out-of-sample predictions

Gaussian Processes: Latent Variable Implementation / Example 2: Classification

Gaussian Processes: Latent Variable Implementation / Example 1: Regression with Student-T distributed noise / Prediction using .conditional

Marginal Likelihood Implementation / Example: Regression with white, Gaussian noise / Using .conditional

Example 1: A hierarchical HSGP, a more custom model / Looking for a beginner’s introduction? / Out-of-sample predictions

Gaussian Processes: HSGP Reference & First Steps / Example 1: Basic HSGP Usage / Define and fit the HSGP model

Gaussian Processes: HSGP Reference & First Steps / Example 1: Basic HSGP Usage / Example 2: Working with HSGPs as a parametric, linear model / Out-of-sample predictions

Interpreting the results

Discrete Choice and Random Utility Models / Choosing Crackers over Repeated Choices: Mixed Logit Model

Discrete Choice and Random Utility Models / Experimental Model: Adding Correlation Structure

Discrete Choice and Random Utility Models / Improved Model: Adding Alternative Specific Intercepts

Discrete Choice and Random Utility Models / Experimental Model: Adding Correlation Structure / Market Inteventions and Predicting Market Share

Discrete Choice and Random Utility Models / The Basic Model

Ordinal Scales and Survey Data / Fit a variety of Model Specifications / Bayesian Particularities

Ordinal Scales and Survey Data / Liddell and Kruschke’s IMDB movie Ratings Data

Out-Of-Sample Predictions / Generate Out-Of-Sample Predictions

Out-Of-Sample Predictions / Model Decision Boundary

Simpson’s paradox and mixed models / Model 2: Independent slopes and intercepts model / Visualisation

Simpson’s paradox and mixed models / Model 1: Basic linear regression / Visualisation

Simpson’s paradox and mixed models / Model 3: Hierarchical regression / Visualise

A Primer on Bayesian Methods for Multilevel Modeling / Adding group-level predictors / Prediction

Bayesian Missing Data Imputation / Bayesian Imputation

Bayesian Missing Data Imputation / Hierarchical Structures and Data Imputation

Bayesian Missing Data Imputation / Bayesian Imputation by Chained Equations / PyMC Imputation

Using ModelBuilder class for deploying PyMC models / Standard syntax

Splines / The model / Fit the model

General API quickstart / 4. Posterior Predictive Sampling

General API quickstart / 4.1 Predicting on hold-out data

Dirichlet mixtures of multinomials / Dirichlet-Multinomial Model - Marginalized

Dirichlet mixtures of multinomials / Multinomial model

Old good Gaussian fit

Demonstrating the BYM model on the New York City pedestrian accidents dataset / Posterior predictive checking

Frailty and Survival Regression Models / Accelerated Failure Time Models

Air passengers - Prophet-like model / Part 1: linear trend

Air passengers - Prophet-like model / Part 2: enter seasonality

Forecasting with Structural AR Timeseries / Prediction Step

Forecasting with Structural AR Timeseries / Complicating the Picture / Specifying a Trend Model

Forecasting with Structural AR Timeseries / Specifying the Model

Forecasting with Structural AR Timeseries / Complicating the picture further / Specifying the Trend + Seasonal Model

Forecasting with Structural AR Timeseries / Complicating the Picture / Wrapping our model into a function

Multivariate Gaussian Random Walk / Model

Time Series Models Derived From a Generative Graph / Motivation / Define AR(2) Process / Posterior Predictive / Out of Sample Predictions

Time Series Models Derived From a Generative Graph / Motivation / Define AR(2) Process / Posterior Predictive

Time Series Models Derived From a Generative Graph / Motivation / Define AR(2) Process / Posterior Predictive / Conditional and Unconditional Posteriors

Bayesian Vector Autoregressive Models / Adding a Bayesian Twist: Hierarchical VARs

Bayesian Vector Autoregressive Models / Handling Multiple Lags and Different Dimensions

Non-Linear Change Trajectories / A Minimal Model

Non-Linear Change Trajectories / Adding in Polynomial Time

Non-Linear Change Trajectories / Behaviour over time

Non-Linear Change Trajectories / Comparing Trajectories across Gender

Modelling Change over Time. / Model controlling for Peer Effects

Modelling Change over Time. / The Unconditional Mean Model

Modelling Change over Time. / The Uncontrolled Effects of Parental Alcoholism

Modelling Change over Time. / Unconditional Growth Model

Stochastic Volatility model / Fit Model

Variational Inference: Bayesian Neural Networks / Lets look at what the classifier has learned

Variational Inference: Bayesian Neural Networks / Bayesian Neural Networks in PyMC / Variational Inference: Scaling model complexity

Expand for references to pymc.sample_prior_predictive

Generalized Extreme Value Distribution / Prior Predictive Checks

Model building and expansion for golf putting / Geometry-based model / Prior Predictive Checks

Reliability Statistics and Predictive Calibration / Bayesian Modelling of Reliability Data / Direct PYMC implementation of Weibull Survival

Introduction to Bayesian A/B Testing / Bernoulli Conversions / Prior predictive checks

Introduction to Bayesian A/B Testing / Value Conversions

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Double/Debiased Machine Learning and Frisch-Waugh-Lovell / Applying Debiased ML Methods

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Non-Confounded Inference: NHEFS Data / Propensity Score Modelling

Bayesian Non-parametric Causal Inference / Causal Inference and Propensity Scores / Non-Confounded Inference: NHEFS Data / Regression with Propensity Scores

Counterfactual inference: calculating excess deaths due to COVID-19 / Prior predictive check

Interrupted time series analysis / Prior predictive check

Interventional distributions and graph mutation with the do-operator / Three different causal DAGs / Interventional distributions, P(y|\operatorname{do}(x=2))

Interventional distributions and graph mutation with the do-operator / Three different causal DAGs

Bayes Factors and Marginal Likelihood / Savage-Dickey Density Ratio

Baby Births Modelling with HSGPs / EDA and Feature Engineering / Prior Predictive Checks

Example 1: A hierarchical HSGP, a more custom model / Example 2: An HSGP that exploits Kronecker structure / Prior predictive checks

Example 1: A hierarchical HSGP, a more custom model / Looking for a beginner’s introduction? / Prior predictive checks

Gaussian Processes: HSGP Reference & First Steps / Example 1: Basic HSGP Usage / Example 2: Working with HSGPs as a parametric, linear model / Model structure

Discrete Choice and Random Utility Models / Choosing Crackers over Repeated Choices: Mixed Logit Model

Discrete Choice and Random Utility Models / Experimental Model: Adding Correlation Structure

Discrete Choice and Random Utility Models / Improved Model: Adding Alternative Specific Intercepts

Discrete Choice and Random Utility Models / The Basic Model

Ordinal Scales and Survey Data / Liddell and Kruschke’s IMDB movie Ratings Data

A Primer on Bayesian Methods for Multilevel Modeling / Conventional approaches

Bayesian Missing Data Imputation / Bayesian Imputation

Bayesian Missing Data Imputation / Hierarchical Structures and Data Imputation

Bayesian Missing Data Imputation / Bayesian Imputation by Chained Equations / PyMC Imputation

Using ModelBuilder class for deploying PyMC models / Standard syntax

Splines / The model / Fit the model

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways / Bayesian Inference with Gradients / Simulate with Pytensor Scan / Check Time Steps

Frailty and Survival Regression Models / Accelerated Failure Time Models

Air passengers - Prophet-like model / Part 1: linear trend

Air passengers - Prophet-like model / Part 2: enter seasonality

Forecasting with Structural AR Timeseries / Complicating the Picture / Specifying a Trend Model

Forecasting with Structural AR Timeseries / Specifying the Model

Forecasting with Structural AR Timeseries / Complicating the picture further / Specifying the Trend + Seasonal Model

Forecasting with Structural AR Timeseries / Complicating the Picture / Wrapping our model into a function

Time Series Models Derived From a Generative Graph / Motivation / Define AR(2) Process / Prior

Bayesian Vector Autoregressive Models / Adding a Bayesian Twist: Hierarchical VARs

Bayesian Vector Autoregressive Models / Handling Multiple Lags and Different Dimensions

Non-Linear Change Trajectories / A Minimal Model

Non-Linear Change Trajectories / Adding in Polynomial Time

Non-Linear Change Trajectories / Behaviour over time

Non-Linear Change Trajectories / Comparing Trajectories across Gender

Modelling Change over Time. / Model controlling for Peer Effects

Modelling Change over Time. / The Unconditional Mean Model

Modelling Change over Time. / The Uncontrolled Effects of Parental Alcoholism

Modelling Change over Time. / Unconditional Growth Model

Stochastic Volatility model / Checking the model

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Sampling functions#

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