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

7.5 Zero-Inflated and hurdle models

When counting things, like cars on a road, stars in the sky, moles on your skin, or virtually anything else, one option is to not count a thing, that is, to get zero. The number zero can generally occur for many reasons; we get a zero because we were counting red cars and a red car did not go down the street or because we missed it. If we use a Poisson or NegativeBinomial distribution to model such data, we will notice that the model generates fewer zeros compared to the data. How do we fix that? We may try to address the exact cause of our model predicting fewer zeros than the observed and include that factor in the model. But, as is often the case, it may be enough, and simpler, to assume that we have a mixture of two processes:

  • One modeled by a discrete distribution with probability

  • One giving extra zeros with probability 1

In some texts, you will find that represents the extra zeros instead of 1 . This is not a big deal;...