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

4.10 Summary

In this chapter, we have learned about linear regression, which aims to model the relationship between a dependent variable and an independent variable. We have seen how to use PyMC to fit a linear regression model and how to interpret the results and make plots that we can share with different audiences.

Our first example was a model with a Gaussian response. But then we saw that this is just one assumption and we can easily change it to deal with non-Gaussian responses, such as count data, using a NegativeBinomial regression model or a logistic regression model for binary data. We saw that when doing so we also need to set an inverse link function to map the linear predictor to the response variable. Using a Student’s t-distribution as the likelihood can be useful for dealing with outliers. We spent most of the chapter modeling the mean as a linear function of the independent variable, but we learned that we can also model other parameters, like the variance. This...