1st Edition

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

516 Pages 87 B/W Illustrations
by CRC Press

516 Pages
by CRC Press

Also available as eBook on:

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.

Prologue
Probability of a Defective: Binomial Data
Brass Alloy Zinc Content: Normal 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
Identifiability and Noninformative Data

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

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

Simulations
Generating Random Samples
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

### Biography

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.

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