Bayesian Regression and Model Selection

Overview

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Master Bayesian modeling through Bayesian linear regression, generalized linear models, hierarchical models and model selection. This course will deepen your understanding of modeling techniques and the importance of the prior when contrasted with traditional frequentist modeling approaches. You will understand the benefits of hierarchical models and how they automatically identify the right amount of pooling between data to provide a balance between the complete and no pooling approaches. You will learn how to apply posterior predictive checks for model selection and understand the Occam’s razor principle. This course combines theoretical modeling foundations with hands-on implementations.

Syllabus

Bayesian Regression - Simple and Multiple Linear Models

Welcome to Bayesian Regression and Model Selection! In this module, we will introduce the Bayesian linear regression. We will see how we can place priors on the coefficients of the models and what we can learn from their posteriors. We will also learn how to define and infer the posteriors of a Bayesian linear regression with pymc.

Hierarchical Bayesian Models

In this module, we will see how hierarchical models make it easy to deal with categorical data, especially when these data are nested. We will see how they automatically identify the right amount of pooling between data to provide a balance between the complete and no pooling approaches.

Bayesian Logistic Regression and Generalized Linear Models (GLMs)

In this module, we will extend the Bayesian linear regression to be able to deal with binary (categorical) and count data. We will see the Bernoulli likelihood for the Bayesian logistic regression and how we can extend it to more than two categories through the categorical likelihood. Finally, we will see the Bayesian Poisson regression (and other options) for count data.

Bayesian Model Selection & Comparison

In this module, we will see the basic notions behind model selection and the philosophical and practical differences between frequentists and Bayesians on the topic. We will understand the difference between the posterior distribution of the model parameters and the posterior predictive distributions. The latter will lead us to the ideas of posterior predictive checks and model coverage.