1st Edition

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

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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.

**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 VectorsAppendix B: ProbabilityAppendix 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.BIDAalso should be strongly considered as a primary text by teachers of introductory courses in applied Bayesian inference. … The writing inBIDAis clear, accurate, and easy to follow.

—Jerome P. Reiter,The American Statistician, November 2011I 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 2011If 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 2011I 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 2011This 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), 79Unlike 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