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

9.4 Constant and linear response

By default, PyMC-BART will fit trees that return a single value at each leaf node. This is a simple approach that usually works just fine. However, it is important to understand its implications. For instance, this means that predictions for any value outside the range of the observed data used to fit the model will be constants. To see this, go back and check Figure 9.2. This tree will return 1.9 for any value below c1. Notice that this will still be the case if we, instead, sum a bunch of trees, because summing a bunch of constant values results in yet another constant value.

Whether this is a problem or not is up to you and the context in which you apply the BART model. Nevertheless, PyMC-BART offers a response argument that you pass to the BART random variable. Its default value is "constant". You can change it to "linear", in which case PyMC-BART will return a linear fit at each leaf node or "mix", which will propose...