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

9.2 BART models

A Bayesian additive regression trees (BART) model is a sum of m trees that we use to approximate a function [Chipman et al.2010]. To complete the model, we need to set priors over trees. The main function of such priors is to prevent overfitting while retaining the flexibility that trees provide. Priors are designed to keep the individual trees relatively shallow and the values at the leaf nodes relatively small.

PyMC does not support BART models directly but we can use PyMC-BART, a Python module that extends PyMC functionality to support BART models. PyMC-BART offers:

  • A BART random variable that works very similar to other distributions in PyMC like pm.Normal, pm.Poisson, etc.

  • A sampler called PGBART as trees cannot be sampled with PyMC’s default step methods such as NUTS or Metropolis.

  • The following utility functions to help work with the result of a BART model:

    • pmb.plot_pdp: A function to generate partial dependence plots [Friedman, ...