Bayesian analysis with Python : a practical guide to probabilistic modeling / Osvaldo Martin ; foreword by: Christopher Fonnesbeck,Thomas Wiecki.

Format:

Book

Author/Creator:

Martin, Osvaldo, author.

Contributor:

Fonnesbeck, Christopher

Wiecki, Thomas

Series:

Expert insight

Language:

English

Subjects (All):

Python (Computer program language).

Natural language processing (Computer science).

Bayesian statistical decision theory.

Physical Description:

1 online resource (395 pages)

Edition:

Third edition.

Place of Publication:

Birmingham, England : Packt Publishing, January 2024

Biography/History:

Martin Osvaldo: Osvaldo Martin is a researcher at CONICET, in Argentina. He has experience using Markov Chain Monte Carlo methods to simulate molecules and perform Bayesian inference. He loves to use Python to solve data analysis problems. He is especially motivated by the development and implementation of software tools for Bayesian statistics and probabilistic modeling. He is an open-source developer, and he contributes to Python libraries like PyMC, ArviZ and Bambi among others. He is interested in all aspects of the Bayesian workflow, including numerical methods for inference, diagnosis of sampling, evaluation and criticism of models, comparison of models and presentation of results.

Summary:

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.

Contents:

Cover

Copyright

Foreword

Contributors

Table of Contents

Preface

Who this book is for

What this book covers

What's new in this edition?

Installation instructions

Conventions used

Chapter 1: Thinking Probabilistically

Statistics, models, and this book's approach

Working with data

Bayesian modeling

A probability primer for Bayesian practitioners

Sample space and events

Random variables

Discrete random variables and their distributions

Continuous random variables and their distributions

Cumulative distribution function

Conditional probability

Expected values

Bayes' theorem

Interpreting probabilities

Probabilities, uncertainty, and logic

Single-parameter inference

The coin-flipping problem

Choosing the likelihood

Choosing the prior

Getting the posterior

The influence of the prior

How to choose priors

Communicating a Bayesian analysis

Model notation and visualization

Summarizing the posterior

Summary

Exercises

Chapter 2: Programming Probabilistically

Probabilistic programming

Flipping coins the PyMC way

Posterior-based decisions

Savage-Dickey density ratio

Region Of Practical Equivalence

Loss functions

Gaussians all the way down

Gaussian inferences

Posterior predictive checks

Robust inferences

Degrees of normality

A robust version of the Normal model

InferenceData

Groups comparison

The tips dataset

Cohen's d

Probability of superiority

Posterior analysis of mean differences

Chapter 3: Hierarchical Models

Sharing information, sharing priors

Hierarchical shifts

Water quality

Shrinkage

Hierarchies all the way up

Chapter 4: Modeling with Lines

Simple linear regression

Linear bikes.

Interpreting the posterior mean

Interpreting the posterior predictions

Generalizing the linear model

Counting bikes

Robust regression

Logistic regression

The logistic model

Classification with logistic regression

Interpreting the coefficients of logistic regression

Variable variance

Hierarchical linear regression

Centered vs. noncentered hierarchical models

Multiple linear regression

Chapter 5: Comparing Models

The balance between simplicity and accuracy

Many parameters (may) lead to overfitting

Too few parameters lead to underfitting

Measures of predictive accuracy

Information criteria

Akaike Information Criterion

Widely applicable information criteria

Other information criteria

Cross-validation

Approximating cross-validation

Calculating predictive accuracy with ArviZ

Model averaging

Bayes factors

Some observations

Calculation of Bayes factors

Analytically

Sequential Monte Carlo

Savage-Dickey ratio

Bayes factors and inference

Regularizing priors

Chapter 6: Modeling with Bambi

One syntax to rule them all

The bikes model, Bambi's version

Polynomial regression

Splines

Distributional models

Categorical predictors

Categorical penguins

Relation to hierarchical models

Interactions

Interpreting models with Bambi

Variable selection

Projection predictive inference

Projection predictive with Kulprit

Chapter 7: Mixture Models

Understanding mixture models

Finite mixture models

The Categorical distribution

The Dirichlet distribution

Chemical mixture

The non-identifiability of mixture models

How to choose K

Zero-Inflated and hurdle models

Zero-Inflated Poisson regression

Hurdle models.

Mixture models and clustering

Non-finite mixture model

Dirichlet process

Continuous mixtures

Some common distributions are mixtures

Chapter 8: Gaussian Processes

Linear models and non-linear data

Modeling functions

Multivariate Gaussians and functions

Covariance functions and kernels

Gaussian processes

Gaussian process regression

Gaussian process regression with PyMC

Setting priors for the length scale

Gaussian process classification

GPs for space flu

Cox processes

Coal mining disasters

Red wood

Regression with spatial autocorrelation

Hilbert space GPs

HSGP with Bambi

Chapter 9: Bayesian Additive Regression Trees

Decision trees

BART models

Bartian penguins

Partial dependence plots

Individual conditional plots

Variable selection with BART

Distributional BART models

Constant and linear response

Choosing the number of trees

Chapter 10: Inference Engines

Inference engines

The grid method

Quadratic method

Markovian methods

Monte Carlo

Markov chain

Metropolis-Hastings

Hamiltonian Monte Carlo

Diagnosing the samples

Convergence

Trace plot

Rank plot

, (R hat)

Effective Sample Size (ESS)

Monte Carlo standard error

Divergences

Keep calm and keep trying

Chapter 11: Where to Go Next

Other Books You May Enjoy

Index.

Notes:

Includes index.

Description based on print version record.

ISBN:

1-80512-541-9

OCLC:

1424953518