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Bayesian Ideas and Data Analysis
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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

About the Author

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.

Reviews

! despite my obvious biases and prejudices, 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 (Universite 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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