Book Image

Bayesian Analysis with Python - Third Edition

By : Osvaldo Martin
Book Image

Bayesian Analysis with Python - Third Edition

By: Osvaldo Martin

Overview of this book

The third edition of Bayesian Analysis with Python serves as an introduction to the main concepts of applied Bayesian modeling using PyMC, a state-of-the-art probabilistic programming library, and other libraries that support and facilitate modeling like ArviZ, for exploratory analysis of Bayesian models; Bambi, for flexible and easy hierarchical linear modeling; PreliZ, for prior elicitation; PyMC-BART, for flexible non-parametric regression; and Kulprit, for variable selection. In this updated edition, a brief and conceptual introduction to probability theory enhances your learning journey by introducing new topics like Bayesian additive regression trees (BART), featuring updated examples. Refined explanations, informed by feedback and experience from previous editions, underscore the book's emphasis on Bayesian statistics. You will explore various models, including hierarchical models, generalized linear models for regression and classification, mixture models, Gaussian processes, and BART, using synthetic and real datasets. By the end of this book, you will possess a functional understanding of probabilistic modeling, enabling you to design and implement Bayesian models for your data science challenges. You'll be well-prepared to delve into more advanced material or specialized statistical modeling if the need arises.
Table of Contents (15 chapters)
Preface
12
Bibliography
13
Other Books You May Enjoy
14
Index

5.1 Posterior predictive checks

We have previously introduced and discussed posterior predictive checks as a way to assess how well a model explains the data used to fit a model. The purpose of this type of testing is not to determine whether a model is incorrect; we already know this! The goal of the exercise is to understand how well we are capturing the data. By performing posterior predictive checks, we aim to better understand the limitations of a model. Once we understand the limitations, we can simply acknowledge them or try to remove them by improving the model. It is expected that a model will not be able to reproduce all aspects of a problem and this is usually not a problem as models are built with a purpose in mind. As different models often capture different aspects of data, we can compare models using posterior predictive checks.

Let’s look at a simple example. We have a dataset with two variables, x and y. We are going to fit these data with a linear model:

y = 𝛼 + 𝛽x

We...