Bayesian Analysis with Python - Third Edition

A practical guide to probabilistic modeling

Osvaldo Martin 지음

Packt(GCO Science) 2024년 01월 31일 출간

작품소개

책소개

Learn the fundamentals of Bayesian modeling using state-of-the-art Python libraries, such as PyMC, ArviZ, Bambi, and more, guided by an experienced Bayesian modeler who contributes to these libraries

▶Book Description
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.

▶What You Will Learn
⦁ Build probabilistic models using PyMC and Bambi
⦁ Analyze and interpret probabilistic models with ArviZ
⦁ Acquire the skills to sanity-check models and modify them if necessary
⦁ Build better models with prior and posterior predictive checks
⦁ Learn the advantages and caveats of hierarchical models
⦁ Compare models and choose between alternative ones
⦁ Interpret results and apply your knowledge to real-world problems
⦁ Explore common models from a unified probabilistic perspective
⦁ Apply the Bayesian framework's flexibility for probabilistic thinking

목차

▶ TABLE of CONTENTS
1. Thinking Probabilistically
2. Programming Probabilistically
3. Hierarchical Models
4. Modeling with Lines
5. Comparing Models
6. Modeling with Bambi
7. Mixture Models
8. Gaussian Processes
9. Bayesian Additive Regression Trees
10. Inference Engines
11. Where to Go Next

책 속으로

▶ What this book covers
⦁ Chapter 1, Thinking Probabilistically, covers the basic concepts of Bayesian statistics and its implications for data analysis. This chapter contains most of the foundational ideas used in the rest of the book.
⦁ Chapter 2, Programming Probabilistically, revisits the concepts from the previous chapter from a more computational perspective. The PyMC probabilistic programming library and ArviZ, a Python library for exploratory analysis of Bayesian models are introduced.
⦁ Chapter 3, Hierarchical Models, illustrates the core ideas of hierarchical models through examples.
⦁ Chapter 4, Modeling with Lines, covers the basic elements of linear regression, a very widely used model and the building block of more complex models, and then moves into generalizing linear models to solve many data analysis problems.
⦁ Chapter 5, Comparing Models, discusses how to compare and select models using posterior predictive checks, LOO, and Bayes factors. The general caveats of these methods are discussed and model averaging is also illustrated.
⦁ Chapter 6, Modeling with Bambi, introduces Bambi, a Bayesian library built on top of PyMC that simplifies working with generalized linear models. In this chapter, we will also discuss variable selection and new models like splines.
⦁ Chapter 7, Mixture Models, discusses how to add flexibility to models by mixing simpler distributions to build more complex ones. The first non-parametric model in the book is also introduced: the Dirichlet process.
⦁ Chapter 8, Gaussian Processes, covers the basic idea behind Gaussian processes and how to use them to build non-parametric models over functions for a wide array of problems.
⦁ Chapter 9, Bayesian Additive Regression Trees, introduces readers to a flexible regression model that combines decision trees and Bayesian modeling techniques. The chapter will cover the key features of BART, including its flexibility in capturing non-linear relationships between predictors and outcomes and how it can be used for variable selection.
⦁ Chapter 10, Inference Engines, provides an introduction to methods for numerically approximating the posterior distribution, as well as a very important topic from the practitioner’s perspective: how to diagnose the reliability of the approximated posterior.
⦁ Chapter 11, Where to Go Next?, provides a list of resources to keep learning from beyond this book, and a concise farewell speech.

출판사 서평

ayesian statistics has been developing for more than 250 years. During this time, it has enjoyed as much recognition and appreciation as it has faced disdain and contempt. Throughout the last few decades, it has gained more and more attention from people in statistics and almost all the other sciences, engineering, and even outside the boundaries of the academic world. This revival has been possible due to theoretical and computational advancements developed mostly throughout the second half of the 20th century. Indeed, modern Bayesian statistics is mostly computational statistics. The necessity for flexible and transparent models and a more intuitive interpretation of statistical models and analysis has only contributed to the trend.
In this book, our focus will be on a practical approach to Bayesian statistics and we will not delve into discussions about the frequentist approach or its connection to Bayesian statistics. This decision is made to maintain a clear and concise focus on the subject matter. If you are interested in that perspective, Doing Bayesian Data Analysis may be the book for you [Kruschke, 2014]. We also avoid philosophical discussions, not because they are not interesting or relevant, but because this book aims to be a practical guide to Bayesian data analysis. One good reading for such discussion is Clayton [2021].
We follow a modeling approach to statistics. We will learn how to think in terms of probabilistic models and apply Bayes’ theorem to derive the logical consequences of our models and data. The approach will also be computational; models will be coded using PyMC [Abril-Pla et al., 2023] and Bambi [Capretto et al., 2022]. These are libraries for Bayesian statistics that hide most of the mathematical details and computations from the user. We will then use ArviZ [Kumar et al., 2019], a Python package for exploratory analysis of Bayesian models, to better understand our results. We will also be assisted by other libraries in the Python ecosystem, including PreliZ [Icazatti et al., 2023] for prior elicitation,
Kulprit for variable selection, and PyMC-BART [Quiroga et al., 2022] for flexible regression. And of course, we will also use common tools from the standard Python Data stack, like NumPy [Harris et al., 2020], matplotlib [Hunter, 2007], Pandas [Wes McKinney, 2010], etc. Bayesian methods are theoretically grounded in probability theory, and so it’s no wonder that many books about Bayesian statistics is full of mathematical formulas requiring a certain level of mathematical sophistication. Learning the mathematical foundations of statistics will certainly help you build better models and gain intuition about problems, models, and results. Nevertheless, libraries such as PyMC allow us to learn and do Bayesian statistics with only a modest amount of mathematical knowledge, as you will be able to verify yourself throughout this book.

작가정보

저자(글) Osvaldo Martin

Osvaldo Martin is a researcher at The National Scientific and Technical Research Council (CONICET), in Argentina. He has worked on structural bioinformatics of biomolecules and has used Markov Chain Monte Carlo methods to simulate molecular systems. He is currently working on computational methods for Bayesian statistics and probabilistic programming. He has taught courses about structural bioinformatics, data science, and Bayesian data analysis. He was also the head of the organizing committee of PyData San Luis (Argentina) 2017, the first PyData in LatinAmerica. He contributed to many open-source projects, including ArviZ, Bambi, Kulprit, PreliZ, and PyMC.