Bayesian Analysis with Python - Third Edition

✍ Scribed by Osvaldo Martin

• Publisher: Packt Publishing
• Year: 2024
• Tongue: English
• Leaves: 399
• Series: EXPERT INSIGHT
• Edition: 3
• Category: Library

✦ Synopsis

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 Key Features: Conduct Bayesian data analysis with step-by-step guidance Gain insight into a modern, practical, and computational approach to Bayesian statistical modeling Enhance your learning with best practices through sample problems and practice exercises Purchase of the print or Kindle book includes a free PDF eBook. 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…

✦ Table of Contents

Bayesian Analysis with Python - Third Edition
Bayesian Analysis with Python Third Edition
Preface
Chapter 1 Thinking Probabilistically
1.1 Statistics, models, and this book’s approach
1.2 Working with data
1.3 Bayesian modeling
1.4 A probability primer for Bayesian practitioners
1.5 Interpreting probabilities
1.6 Probabilities, uncertainty, and logic
1.7 Single-parameter inference
1.8 How to choose priors
1.9 Communicating a Bayesian analysis
1.10 Summary
1.11 Exercises
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Chapter 2 Programming Probabilistically
2.1 Probabilistic programming
2.2 Summarizing the posterior
2.3 Posterior-based decisions
2.4 Gaussians all the way down
2.5 Posterior predictive checks
2.6 Robust inferences
2.7 InferenceData
2.8 Groups comparison
2.9 Summary
2.10 Exercises
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Chapter 3 Hierarchical Models
3.1 Sharing information, sharing priors
3.2 Hierarchical shifts
3.3 Water quality
3.4 Shrinkage
3.5 Hierarchies all the way up
3.6 Summary
3.7 Exercises
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Chapter 4 Modeling with Lines
4.1 Simple linear regression
4.2 Linear bikes
4.3 Generalizing the linear model
4.4 Counting bikes
4.5 Robust regression
4.6 Logistic regression
4.7 Variable variance
4.8 Hierarchical linear regression
4.9 Multiple linear regression
4.10 Summary
4.11 Exercises
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Chapter 5 Comparing Models
5.1 Posterior predictive checks
5.2 The balance between simplicity and accuracy
5.3 Measures of predictive accuracy
5.4 Calculating predictive accuracy with ArviZ
5.5 Model averaging
5.6 Bayes factors
5.7 Bayes factors and inference
5.8 Regularizing priors
5.9 Summary
5.10 Exercises
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Chapter 6 Modeling with Bambi
6.1 One syntax to rule them all
6.2 The bikes model, Bambi’s version
6.3 Polynomial regression
6.4 Splines
6.5 Distributional models
6.6 Categorical predictors
6.7 Interactions
6.8 Interpreting models with Bambi
6.9 Variable selection
6.10 Summary
6.11 Exercises
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Chapter 7 Mixture Models
7.1 Understanding mixture models
7.2 Finite mixture models
7.3 The non-identifiability of mixture models
7.4 How to choose K
7.5 Zero-Inflated and hurdle models
7.6 Mixture models and clustering
7.7 Non-finite mixture model
7.8 Continuous mixtures
7.9 Summary
7.10 Exercises
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Chapter 8 Gaussian Processes
8.1 Linear models and non-linear data
8.2 Modeling functions
8.3 Multivariate Gaussians and functions
8.4 Gaussian processes
8.5 Gaussian process regression
8.6 Gaussian process regression with PyMC
8.7 Gaussian process classification
8.8 Cox processes
8.9 Regression with spatial autocorrelation
8.10 Hilbert space GPs
8.11 Summary
8.12 Exercises
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Chapter 9 Bayesian Additive Regression Trees
9.1 Decision trees
9.2 BART models
9.3 Distributional BART models
9.4 Constant and linear response
9.5 Choosing the number of trees
9.6 Summary
9.7 Exercises
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Chapter 10 Inference Engines
10.1 Inference engines
10.2 The grid method
10.3 Quadratic method
10.4 Markovian methods
10.5 Sequential Monte Carlo
10.6 Diagnosing the samples
10.7 Convergence
10.8 Effective Sample Size (ESS)
10.9 Monte Carlo standard error
10.10 Divergences
10.11 Keep calm and keep trying
10.12 Summary
10.13 Exercises
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Chapter 11 Where to Go Next
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Bibliography
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