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

2.1 Probabilistic programming

Bayesian statistics is conceptually very simple. We have the knowns and the unknowns, and we use Bayes’ theorem to condition the latter on the former. If we are lucky, this process will reduce the uncertainty about the unknowns. Generally, we refer to the knowns as data and treat it like constants, and the unknowns as parameters and treat them as random variables.

Although conceptually simple, fully probabilistic models often lead to analytically intractable expressions. For many years, this was a real problem and one of the main issues that hindered the adoption of Bayesian methods beyond some niche applications. The arrival of the computational era and the development of numerical methods that, at least in principle, can be used to solve any inference problem, have dramatically transformed the Bayesian data analysis practice. We can think of these numerical methods as universal inference engines. The possibility of automating the inference process...