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

9.3 Distributional BART models

As we saw in Chapter 6, for generalized linear models, we are not restricted to creating linear models for the mean or location parameter; we can also model other parameters, for example, the standard deviation of a Gaussian or even both the mean and standard deviation. The same applies to BART models.

To exemplify this, let’s model the bike dataset. We will use rented as the response variable and hour, temperature, humidity, and workday as predictor variables. As we did previously, we are going to use a NegativeBinomial distribution as likelihood. This distribution has two parameters μ and alpha. We are going to use a sum of trees for both parameters. The following code block shows the model:

Code 9.5

with pm.Model() as model_bb: 
    μ = pmb.BART("μ", X, np.log(Y), shape=(2, 348), separate_trees=True) 
    pm.NegativeBinomial('yl', np.exp(μ...