Bayesian Ideas and Data Analysis

Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians

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Features

    • Covers a large number of statistical models
    • Emphasizes the elicitation of reasonable prior information
    • Explores numerical approximations via simulation
    • Uses WinBUGS and R for computational problems
    • Reviews basic concepts of matrix algebra and probability
    • Includes numerous exercises and real-world examples throughout
    • Provides data, programming code, and other materials at www.stat.unm.edu/~fletcher

    Summary

    Emphasizing the use of WinBUGS and R to analyze real data, Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians presents statistical tools to address scientific questions. It highlights foundational issues in statistics, the importance of making accurate predictions, and the need for scientists and statisticians to collaborate in analyzing data. The WinBUGS code provided offers a convenient platform to model and analyze a wide range of data.

    The first five chapters of the book contain core material that spans basic Bayesian ideas, calculations, and inference, including modeling one and two sample data from traditional sampling models. The text then covers Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) simulation. After discussing linear structures in regression, it presents binomial regression, normal regression, analysis of variance, and Poisson regression, before extending these methods to handle correlated data. The authors also examine survival analysis and binary diagnostic testing. A complementary chapter on diagnostic testing for continuous outcomes is available on the book’s website. The last chapter on nonparametric inference explores density estimation and flexible regression modeling of mean functions.

    The appropriate statistical analysis of data involves a collaborative effort between scientists and statisticians. Exemplifying this approach, Bayesian Ideas and Data Analysis focuses on the necessary tools and concepts for modeling and analyzing scientific data.

    Data sets and codes are provided on a supplemental website.

    Table of Contents

    Prologue
    Probability of a Defective: Binomial Data
    Brass Alloy Zinc Content: Normal Data
    Armadillo Hunting: Poisson Data
    Abortion in Dairy Cattle: Survival Data
    Ache Hunting with Age Trends
    Lung Cancer Treatment: Log-Normal Regression
    Survival with Random Effects: Ache Hunting

    Fundamental Ideas I
    Simple Probability Computations
    Science, Priors, and Prediction
    Statistical Models
    Posterior Analysis
    Commonly Used Distributions

    Integration versus Simulation
    Introduction
    WinBUGS I: Getting Started
    Method of Composition
    Monte Carlo Integration
    Posterior Computations in R

    Fundamental Ideas II
    Statistical Testing
    Exchangeability
    Likelihood Functions
    Sufficient Statistics
    Analysis Using Predictive Distributions
    Flat Priors
    Jeffreys’ Priors
    Bayes Factors
    Other Model Selection Criteria
    Normal Approximations to Posteriors
    Bayesian Consistency and Inconsistency
    Hierarchical Models
    Some Final Comments on Likelihoods
    Identifiability and Noninformative Data

    Comparing Populations
    Inference for Proportions
    Inference for Normal Populations
    Inference for Rates
    Sample Size Determination
    Illustrations: Foundry Data

    Medfly Data
    Radiological Contrast Data
    Reyes Syndrome Data
    Corrosion Data
    Diasorin Data
    Ache Hunting Data
    Breast Cancer Data

    Simulations
    Generating Random Samples
    Traditional Monte Carlo Methods
    Basics of Markov Chain Theory
    Markov Chain Monte Carlo

    Basic Concepts of Regression
    Introduction
    Data Notation and Format
    Predictive Models: An Overview
    Modeling with Linear Structures
    Illustration: FEV Data

    Binomial Regression
    The Sampling Model
    Binomial Regression Analysis
    Model Checking
    Prior Distributions
    Mixed Models
    Illustrations: Space Shuttle Data

    Trauma Data
    Onychomycosis Fungis Data
    Cow Abortion Data

    Linear Regression
    The Sampling Model
    Reference Priors
    Conjugate Priors
    Independence Priors
    ANOVA
    Model Diagnostics
    Model Selection
    Nonlinear Regression
    Illustrations: FEV Data

    Bank Salary Data
    Diasorin Data
    Coleman Report Data
    Dugong Growth Data

    Correlated Data
    Introduction
    Mixed Models
    Multivariate Normal Models
    Multivariate Normal Regression
    Posterior Sampling and Missing Data
    Illustrations: Interleukin Data

    Sleeping Dog Data
    Meta-Analysis Data
    Dental Data

    Count Data
    Poisson Regression
    Over-Dispersion and Mixtures of Poissons
    Longitudinal Data
    Illustrations: Ache Hunting Data

    Textile Faults Data
    Coronary Heart Disease Data
    Foot and Mouth Disease Data

    Time to Event Data
    Introduction
    One-Sample Models
    Two-Sample Data
    Plotting Survival and Hazard Functions
    Illustrations: Leukemia Cancer Data

    Breast Cancer Data

    Time to Event Regression
    Accelerated Failure Time Models
    Proportional Hazards Modeling
    Survival with Random Effects
    Illustrations: Leukemia Cancer Data

    Larynx Cancer Data
    Cow Abortion Data
    Kidney Transplant Data
    Lung Cancer Data
    Ache Hunting Data

    Binary Diagnostic Tests
    Basic Ideas
    One Test, One Population
    Two Tests, Two Populations
    Prevalence Distributions
    Illustrations: Coronary Artery Disease

    Paratuberculosis Data
    Nucleospora Salmonis Data
    Ovine Progressive Pnemonia Data

    Nonparametric Models
    Flexible Density Shapes
    Flexible Regression Functions
    Proportional Hazards Modeling
    Illustrations: Galaxy Data

    ELISA Data for Johnes Disease
    Fungus Data
    Test Engine Data
    Lung Cancer Data

    Appendix A: Matrices and Vectors
    Appendix B: Probability
    Appendix C: Getting Started in R

    References

    Author Bio(s)

    Ronald Christensen is a Professor in the Department of Mathematics and Statistics at the University of New Mexico, Albuquerque. He is also a Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics as well as the former Chair of the ASA Section on Bayesian Statistical Science.

    Wesley Johnson is a Professor in the Department of Statistics at the University of California, Irvine. He is also a Fellow of the ASA and Chair-Elect of the ASA Section on Bayesian Statistical Science.

    Adam Branscum is an Associate Professor in the Department of Public Health at Oregon State University, Corvallis.

    Timothy E. Hanson is an Associate Professor in the Department of Statistics at the University of South Carolina, Columbia.

    Editorial Reviews

    This book provides a good introduction to Bayesian approaches to applied statistical modelling. … The authors have fulfilled their main aim of introducing Bayesian ideas through examples using a large number of statistical models. An interesting feature of this book is the humour of the authors that make it more fun than typical statistics books. In summary, this is a very interesting introductory book, very well organised and has been written in a style that is extremely pleasant and enjoyable to read. Both the statistical concepts and examples are very well explained. In conclusion, I highly recommend this book as both a M.S./Ph.D. course text and as an excellent reference book for anyone interested in Bayesian statistics. A copy of it should certainly appear in every university or, even private, library.
    —Rolando de la Cruz, Journal of Applied Statistics, June 2012

    Bayesian Ideas and Data Analysis (BIDA) is exactly what its title advertises: an introduction to Bayesian approaches to applied statistical modeling. Its authors, who are renowned Bayesian statisticians, present a variety of insightful case studies of Bayesian data analysis, many of which have been drawn from their own research. The book is an excellent purchase for practitioners who are unfamiliar with Bayesian methods and want to learn to use them for their data-based research. BIDA also should be strongly considered as a primary text by teachers of introductory courses in applied Bayesian inference. … The writing in BIDA is clear, accurate, and easy to follow.
    —Jerome P. Reiter, The American Statistician, November 2011

    I liked it very much! … the book is indeed focused on explaining the Bayesian ideas through (real) examples and it covers a lot of regression models, all the way to non-parametrics. It contains a good proportion of WinBUGS and R codes. … The book is pleasant to read, with humorous comments here and there. …
    —Christian Robert (Université Paris-Dauphine) on his blog, October 2011

    If you think that a Bayesian approach to statistical analysis is nice in principle but too complicated in practice, this book may change your mind. The authors’ enthusiasm for the subject is apparent and they have taken care that the text is generally easy to read, with some occasional wry comments that make it more amusing than a typical statistics book. The emphasis is on medical and biological cases, but a range of other applications are covered. …
    There are three useful appendices on matrices and vectors, probability, and getting started in R, which is well chosen, and includes a note on the interface between R and WinBUGS. The exercises are an integral part of the book and are placed throughout the text …
    I think that the book is innovative for two reasons. Firstly, it provides an intermediate-level course in statistics, using the Bayesian paradigm, that could be given to engineers and scientists requiring substantial statistical analysis, as well as material for a course in Bayesian statistics that is typically offered to statistics students. Secondly, it shows how to perform the analyses by using WinBUGS throughout the text. I would use this book as a basis for a course on Bayesian statistics. It is an excellent text for individual study, and students will find it a valuable reference later in their careers.
    —Andrew V. Metcalfe, Journal of the Royal Statistical Society: Series A, Vol. 174, October 2011

    I do believe this book to be more accessible that most Bayesian books … this book could be adequate for the statistics student who has a solid background in statistical concepts and wants to gain more knowledge about the Bayesian approach. … The authors do a good job of providing examples … There are a number of exercises included, which makes the book adequate as a textbook. … There are many samples of WinBUGS code interspersed throughout for the different data examples, which are valuable for someone trying to implement Bayesian methods for data analysis. I found the book easy to read and there are more attempts to liven up the book with humor than the typical textbook.
    —Willis A. Jensen, Journal of Quality Technology, Vol. 43, No. 2, April 2011

    This is a very sound introductory text, and is certainly one which teachers of any course on Bayesian statistics beyond the briefest and most elementary should consider adopting.
    —David J. Hand, International Statistical Review (2011), 79

    Unlike many Bayesian books which did not cover this topic extensively, this new book teaches readers how to illicit informative priors from field experts in great detail. … Straightforward R codes are also provided for pinpointing hyperparameter values … this book is particularly valuable in emphasizing the right approach to elicit prior, an important component of deriving posterior or predictive distribution.
    Another important feature of this new Bayesian textbook is its rich details. …The proofs never skip steps, and are easy to follow for readers taking only one or two semester math stat classes. The well-written text along with more than 70 figures and 50 plus tables add tremendously to the elucidation of the problems discussed in the book. Directly following some examples or important discussion in the text, readers can self-check whether they understand the materials by playing with some exercise problems, most of which are pretty straightforward.
    Christensen et al. provide many WinBUGS codes in the book and a website for readers to download these codes. In addition, the authors introduce how to perform Bayesian inferences using SAS codes on two occasions … The book also recommends some other programs or websites that will facilitate computation …
    This book is also characterized by its humor, … [making] reading this Bayesian book more delightful.
    —Dunlei Cheng, Statistics in Medicine, 2011

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