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

7.7 Non-finite mixture model

For some problems, such as trying to cluster handwritten digits, it is easy to justify the number of groups we expect to find in the data. For other problems, we can have good guesses; for example, we may know that our sample of Iris flowers was taken from a region where only three species of Iris grow, thus using three components is a reasonable starting point. When we are not that sure about the number of components, we can use model selection to help us choose the number of groups. Nevertheless, for other problems, choosing the number of groups a priori can be a shortcoming, or we may instead be interested in estimating this number directly from the data. A Bayesian solution for this type of problem is related to the Dirichlet process.

7.7.1 Dirichlet process

All the models that we have seen so far have been parametric models, meaning models with a fixed number of parameters that we are interested in estimating, like a fixed number of clusters. We...