Sampling functions#

Expand for references to pymc.sample

Categorical regression / Fitting independent trees

Categorical regression / Model Specification

Modeling Heteroscedasticity with BART / Model Specification

Bayesian Additive Regression Trees: Introduction / Biking with BART

Bayesian Additive Regression Trees: Introduction / Coal mining with BART

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

Bayesian Estimation Supersedes the T-Test / Example: Drug trial evaluation

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Full Measurement Model

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Measurement Models / Intermediate Cross-Loading Model

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Measurement Models

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Bayesian Structural Equation Models / Model Complexity and Bayesian Sensitivity Analysis

Generalized Extreme Value Distribution / Inference

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

Estimating parameters of a distribution from awkwardly binned data / Example 6: A non-normal distribution / Model specification

Estimating parameters of a distribution from awkwardly binned data / Example 3: Parameter estimation with two bins together / Model Specification

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

Simpson’s paradox / Model 1: Pooled regression / Conduct inference

Simpson’s paradox / Model 2: Unpooled regression with counfounder included / Conduct inference

Simpson’s paradox / Model 3: Partial pooling model with confounder included / Conduct inference

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

Student-t Process / Poisson data generated by a T process

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

2. ModelA: Auto-impute Missing Values / 2.3 Sample Posterior, View Diagnostics / 2.3.1 Sample Posterior and PPC

1. Model0: Baseline without Missing Values / 1.3 Sample Posterior, View Diagnostics / 1.3.1 Sample Posterior and PPC

GLM: Model Selection / Generate toy datasets / Demonstrate simple linear model / Define model using explicit PyMC method

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

2. Model B: A Better Way - Dirichlet Hyperprior Allocator / 2.3 Sample Posterior, View Diagnostics / 2.3.1 Sample Posterior and PPC

1. Model A: The Wrong Way - Simple Linear Coefficients / 1.3 Sample Posterior, View Diagnostics / 1.3.1 Sample Posterior and PPC

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

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

Splines / Predicting on new data

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

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

Using a custom step method for sampling from locally conjugate posterior distributions / Comparing partial conjugate with full NUTS sampling

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

Different Covariance Functions

Model Specification

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

Linear Regression / (5) Analyse real data

Linear Regression / Simulation-based Validation & Calibration

Categories / Analyze real sample / Analyze the synthetic people

Curves from lines / Example: Cherry Blossom Blooms / Draw some samples from the prior

Categories / Testing / Fit total effect on the synthetic sample

Curves from lines / Polynomial Linear Models / Fitting N-th Order Polynomials to Height / Width Data

BONUS: Full Luxury Bayes / Why would we do this?

The Periodic Table of Confounds / Fork Example: Marriage Rates & Divorce Rates (& Waffle House!) / (3) Statistical Model for Causal Effect of Marriage on Divorce / Run the statistical model on the simulated data

The Periodic Table of Confounds / Continuous Example / Statistical Model for Causal Effect of Age on Divorce Rate

Confounds / Backdoor Criterion / Unstratified (confounded) Model / Fit the unstratified model, ignoring Z (and U)

Confounds / Backdoor Criterion / Stratifying by Z (unconfounded)

Infinite causes, finite data / Penalty Prediction & Model (Mis-) Selection / Simulate the plant growth experiment / Correct adjustment set (not stratifying by F)

Infinite causes, finite data / Outliers and Robust Regression / Fit Least Square Model

Infinite causes, finite data / Penalty Prediction & Model (Mis-) Selection / Simulate the plant growth experiment / Incorrect adjustment set (stratifying by F)

Infinite causes, finite data / Robust Linear Regression Using the Student-t Likelihood

Drawing the Markov Owl 🦉 / Including Judge Effects / Fit the judge model

2012 New Jersey Wine Judgement / Simplest Model / Fit the simple, wine-specific model

Drawing the Markov Owl 🦉 / More complete model, stratify by Wine Origin, O_{X[i]} / Fit the wine origin model

BONUS: Survival Analysis / Statistical Model / Finding reasonable hyperparameter for \alpha

3. Statistical Models / Fitting Direct Causal Effect Model

3. Statistical Models / Statistical models for admissions / Fitting Total Causal Effect Model

Counts and Poisson Regression / Scientific model that includes innovation and technology loss / Determine good prior hyperparams

Confounded Admissions / Direct Effect Estimator (now confounded due to common ability cause) / Fit the (confounded) Direct Effect Model

Confounded Admissions / Sensitivity Analysis: Modeling latent ability confound variable / Fit the latent ability model

Confounded Admissions / Total Effect Estimator / Fit the Total Effect Model

Counts and Poisson Regression / Comparing Models / Model A - Global Intercept model

Counts and Poisson Regression / Comparing Models / Model B - Interaction model

BONUS: Simpons’s Pandora’s Box / Nonlinear Haunting / Partially Stratified Model – \text{logit}(p) = \alpha + \beta_{Z[i]} X_i

BONUS: Simpons’s Pandora’s Box / Nonlinear Haunting / Try a fully-stratified model – \text{logit}(p_i) = \alpha_{Z[i]} + \beta_{Z[i]}X_i

BONUS: Simpons’s Pandora’s Box / Nonlinear Haunting / Unstratified Model – \text{logit}(p_i) = \alpha + \beta X_i

Ethics & Trolley Problem Studies / Ordered Monotonic Predictors / Assessing the Direct Effect of Education: Stratifying by Gender & Age

Ethics & Trolley Problem Studies / What about competing causes? / Fit the gender-stratified model

Ethics & Trolley Problem Studies / Statistical Model / Starting off easy

Case Study: Reed Frog Survival / Building a Multilievel (Hierarchical) Model / Fit the multi-level model

BONUS: Fixed Effects, Multilevel Models, & Mundlak Machines / Random Confounds / Fixed effect Model

Case Study: Reed Frog Survival / Building a Multilievel (Hierarchical) Model / Comparing multi-level and fixed-sigma model / Fixed sigma model

BONUS: Fixed Effects, Multilevel Models, & Mundlak Machines / Random Confounds / Multilevel Model

Case Study: Reed Frog Survival / Including the presence of predators / Multilevel model with predator effects

BONUS: Fixed Effects, Multilevel Models, & Mundlak Machines / Random Confounds / Naive Model

BONUS: Fixed Effects, Multilevel Models, & Mundlak Machines / Random Confounds / Mundlak Machines / Statistical Model

Case Study: Reed Frog Survival / Let’s build a (multi-level) model / What about the prior variance \sigma?

BONUS: Fixed Effects, Multilevel Models, & Mundlak Machines / Latent Mundlak Machine (aka “Full Luxury Bayes”) / 2. Y sub-model

Fertility & Behavior in Bangladesh / Varying districs + urban / Fit the district-urban model

Fertility & Behavior in Bangladesh / Start simple: varying districts

Adding Correlated Features / Model with correlated features / A couple of notes ⚠️

BONUS: Non-centered (aka Transformed) Priors / Example: Devil’s Funnel prior / Centered-prior models

BONUS: Non-centered (aka Transformed) Priors / Non-centered prior

Adding Correlated Features / Previous model – Using uncorrelated urban features

What Motivates Sharing? / Including Predictive Household features / Add observed confounds variables to simulated dataset

What Motivates Sharing? / 3) Statistical Model / Fit Wealth Gifting model on simulated data (validation)

What Motivates Sharing? / 3) Statistical Model / Fitting the social ties model / Notes

Phylogenetic Regression / Two equivalent formulations of Linear Regression / Classic Linear Regression

Gaussian Processes (in the abstract) / Stratify by population size / Prior Predictive / Fit population-only model for comparison

Phylogenetic Regression / From Model to Kernel / Fit the full Phylogentic model.

Phylogenetic Regression / From Model to Kernel / Influence of Group Size on Brain Size

Gaussian Processes (in the abstract) / Distance-based model / Model the data

Gaussian Processes (in the abstract) / Stratify by population size / Prior Predictive

Phylogenetic Regression / From Model to Kernel / Distance-only model / PyMC Implementation

Phylogenetic Regression / Two equivalent formulations of Linear Regression / \text{MVNormal} Linear Regression

Misclassification / Paternity in Himba pastoralist culture / Fit analogous model without accouting for misclassification

Modeling Measurment / Compare causal effects for models that do and do not model measurement error / Fit model that considers no measurement error

Modeling Measurment / Let’s start simpler / Fit the Divorce Measurement Error Model

Modeling Measurment / Let’s start simpler / 4 Submodels / Marriage Rate Measurement Error Model

Measurement Error / Myth: Measurement error can only decrease an effect, not increase

Misclassification / Paternity in Himba pastoralist culture / Fit the model with misclassification error / Notes

BONUS: Floating Point Monsters / Previous Paternity measurement model with log-scaling tricks

Revisiting Phylogenetic Regression / Drawing the missing owl 🦉 / Complete case model for comparison

Revisiting Phylogenetic Regression / Drawing the missing owl 🦉 / 3. Impute G using a G-specific submodels / 3. Fit model that combines phylogeny and M \rightarrow G

Revisiting Phylogenetic Regression / Drawing the missing owl 🦉 / 2. Impute G,M naively, ignoring models for each / Fit the naive imputation model

Revisiting Phylogenetic Regression / Drawing the missing owl 🦉 / 4. Impute B,G,M using a submodel for each

Revisiting Phylogenetic Regression / Drawing the missing owl 🦉 / 3. Impute G using a G-specific submodels / 2. Model that only includes Social group phylogentic interactions

Revisiting Phylogenetic Regression / Drawing the missing owl 🦉 / 3. Impute G using a G-specific submodels / 1. Model that only models effect of body mass on group size M \rightarrow G

GLMs & GLMM & Generalized Linear Habits / Revisiting Modeling Human Height ⚖️ / Fit the dimensionless cylinder model

GLMs & GLMM & Generalized Linear Habits / Revisiting Modeling Human Height ⚖️ / Statistical Model / Fit the statistical model

Population Dynamics / Implement the statistical model / PyMC implementation details

Choices, observation, and learning strategies 🟦🟥 / State-based Model / State-based statistical Model

Bayesian Parametric Survival Analysis / Accelerated failure time models / Log-logistic survival regression

Bayesian Parametric Survival Analysis / Accelerated failure time models / Weibull survival regression

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

Inferring parameters of SDEs using a Euler-Maruyama scheme / Example Model

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

Pathfinder Variational Inference

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

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Full Measurement Model

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Measurement Models / Intermediate Cross-Loading Model

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Measurement Models

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Bayesian Structural Equation Models / Model Complexity and Bayesian Sensitivity Analysis

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

Simpson’s paradox / Model 1: Pooled regression / Visualisation

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

Student-t Process / Poisson data generated by a T process

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

2. ModelA: Auto-impute Missing Values / 2.3 Sample Posterior, View Diagnostics / 2.3.1 Sample Posterior and PPC

1. Model0: Baseline without Missing Values / 1.3 Sample Posterior, View Diagnostics / 1.3.1 Sample Posterior and PPC

1. Model0: Baseline without Missing Values / 1.5 Create PPC Forecast on dfrawx_holdout set / 1.5.2 Sample PPC for yhat

2. ModelA: Auto-impute Missing Values / 2.5 Create PPC Forecast on dfx_holdout set / 2.5.2 Secondly: sample PPC for missing values xk_unobserved in out-of-sample dataset

2. ModelA: Auto-impute Missing Values / 2.5 Create PPC Forecast on dfx_holdout set / 2.5.3 Thirdly: sub the predictions for xk_unobserved into idata and sample PPC for yhat

2. Model B: A Better Way - Dirichlet Hyperprior Allocator / 2.3 Sample Posterior, View Diagnostics / 2.3.1 Sample Posterior and PPC

1. Model A: The Wrong Way - Simple Linear Coefficients / 1.5 Create PPC Forecast on simplified forecast set / Replace dataset with dffx and rebuild

2. Model B: A Better Way - Dirichlet Hyperprior Allocator / 2.5 Create PPC Forecast on simplified forecast set / 2.5.1 Replace dataset with dffx, rebuild, and sample PPC

1. Model A: The Wrong Way - Simple Linear Coefficients / 1.3 Sample Posterior, View Diagnostics / 1.3.1 Sample Posterior and PPC

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

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

Splines / Predicting on new data

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

Different Covariance Functions

Out-of-sample posterior predictions

Posterior Predictive Checks

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

Linear Regression / Simulation-based Validation & Calibration / Test Model Validity with Posterior Predictive Distribution

Categories / Contrast at each height

Curves from lines / Polynomial Linear Models / Fitting N-th Order Polynomials to Height / Width Data

BONUS: Full Luxury Bayes / Simulate interventions with do operator

The Periodic Table of Confounds / Fork Example: Marriage Rates & Divorce Rates (& Waffle House!) / Simulating Interventions / do(M)

🤘 / Run Age Counterfactuals

BONUS: Simpons’s Pandora’s Box / Nonlinear Haunting / Fullly Stratified Model posterior predictions

BONUS: Simpons’s Pandora’s Box / Nonlinear Haunting / Partially Stratified model posterior predictions

Counts and Poisson Regression / Comparing Models / Posterior Predictions

BONUS: Simpons’s Pandora’s Box / Nonlinear Haunting / Unstratified model posterior predictions

Ethics & Trolley Problem Studies / Ordered Monotonic Predictors / Running Counterfactuals

Ethics & Trolley Problem Studies / Statistical Model / Posterior Predictive Distributions

Ethics & Trolley Problem Studies / What about competing causes? / Running Counterfactuals

Gaussian Processes (in the abstract) / Stratify by population size / Prior Predictive / Fit population-only model for comparison

GLMs & GLMM & Generalized Linear Habits / Revisiting Modeling Human Height ⚖️ / Statistical Model / Fit the statistical model

Bayesian Parametric Survival Analysis / Accelerated failure time models / Log-logistic survival regression

Bayesian Parametric Survival Analysis / Accelerated failure time models / Weibull survival regression

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

Inferring parameters of SDEs using a Euler-Maruyama scheme / Example Model

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 / Variational Inference: Scaling model complexity / Mini-batch ADVI

Expand for references to pymc.sample_prior_predictive

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics / Bayesian Structural Equation Models / Model Complexity and Bayesian Sensitivity Analysis

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

2. ModelA: Auto-impute Missing Values / 2.2 Sample Prior Predictive, View Diagnostics

1. Model0: Baseline without Missing Values / 1.2 Sample Prior Predictive, View Diagnostics

2. Model B: A Better Way - Dirichlet Hyperprior Allocator / 2.2 Sample Prior Predictive, View Diagnostics

1. Model A: The Wrong Way - Simple Linear Coefficients / 1.2 Sample Prior Predictive, View Diagnostics

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

Adding Correlated Features / Compare to prior

Adding Correlated Features / Previous model – Using uncorrelated urban features / Demonstrate that feature priors are independent in uncorrelated model

Gaussian Processes (in the abstract) / Distance-based model / Check model with prior-predictive simulation

Gaussian Processes (in the abstract) / Stratify by population size / Prior Predictive

Phylogenetic Regression / From Model to Kernel / Distance-only model / PyMC Implementation

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

Samplers#