bayesian inference basics

This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context.

The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists.

Bayesian Statistics and Marketing describes the basic advantages of the Bayesian approach, detailing the nature of the computational revolution. Examples contained include household and consumer panel data on product purchases and survey data, demand models based on micro-economic theory and random effect models used to pool data among respondents. The book also discusses the theory and practical use of MCMC methods.

Written by the leading experts in the field, this unique book:

• Presents a unified treatment of Bayesian methods in marketing, with common notation and algorithms for estimating the models.
• Provides a self-contained introduction to Bayesian methods.
• Includes case studies drawn from the authors’ recent research to illustrate how Bayesian methods can be extended to apply to many important marketing problems.
• Is accompanied by an R package, bayesm, which implements all of the models and methods in the book and includes many datasets. In addition the book’s website hosts datasets and R code for the case studies.

"I cannot think of a better book for teachers of introductory statistics who want a readable and pedagogically sound text to introduce Bayesian statistics."
—Statistics in Medical Research

"[This book] is written in a lucid conversational style, which is so rare in mathematical writings. It does an excellent job of presenting Bayesian statistics as a perfectly reasonable approach to elementary problems in statistics."
—STATS: The Magazine for Students of Statistics, American Statistical Association

"Bolstad offers clear explanations of every concept and method making the book accessible and valuable to undergraduate and graduate students alike."
—Journal of Applied Statistics

The use of Bayesian methods in applied statistical analysis has become increasingly popular, yet most introductory statistics texts continue to only present the subject using frequentist methods. Introduction to Bayesian Statistics, Second Edition focuses on Bayesian methods that can be used for inference, and it also addresses how these methods compare favorably with frequentist alternatives. Teaching statistics from the Bayesian perspective allows for direct probability statements about parameters, and this approach is now more relevant than ever due to computer programs that allow practitioners to work on problems that contain many parameters.

This book uniquely covers the topics typically found in an introductory statistics book—but from a Bayesian perspective—giving readers an advantage as they enter fields where statistics is used. This Second Edition provides:

• Extended coverage of Poisson and Gamma distributions

• Two new chapters on Bayesian inference for Poisson observations and Bayesian inference for the standard deviation for normal observations

• A twenty-five percent increase in exercises with selected answers at the end of the book

• A calculus refresher appendix and a summary on the use of statistical tables

• New computer exercises that use R functions and Minitab® macros for Bayesian analysis and Monte Carlo simulations

Introduction to Bayesian Statistics, Second Edition is an invaluable textbook for advanced undergraduate and graduate-level statistics courses as well as a practical reference for statisticians who require a working knowledge of Bayesian statistics.

Focusing on Bayesian approaches and computations using simulation-based methods for inference, Time Series: Modeling, Computation, and Inference integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling and analysis, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and emerging topics at research frontiers.

The book presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. The authors also explore the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian tools, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. They illustrate the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, and finance. Data sets, R and MATLAB^® code, and other material are available on the authors’ websites.

Along with core models and methods, this text offers sophisticated tools for analyzing challenging time series problems. It also demonstrates the growth of time series analysis into new application areas.

Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation.

The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties.

Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.