‘Bayesian Methods for Statistical Analysis’ is a book on statistical methods for analysing a wide variety of data. The book consists of 12 chapters, starting with basic concepts and covering numerous topics, including Bayesian estimation, decision theory, prediction, hypothesis testing, hierarchicalBAYESIAN METHODSfor Statistical AnalysisBY BOREK PUZAAustralianNational终 UniversityeVIEWANUeVIEWPublished by anu eviewThe Australian National UniversityActon act 2601, australiaEmail: enquiries. eview@anu.edu.auThistitleisalsoavailableonlineathttp://eview.anu.edu.auNational Library of Australia Cataloguing-in-Publication entryCreatorPuza, Borek, authorTitleBayesian methods for statistical analysis/ Borek PuzaISBN9781921934254( paperback)9781921934261( ebook)SubjectsBayesian statistical decision theoryStatistical decisionDewey nu519.542All rights reserved. No part of this publication may be reproduced, stored in a retrieval systemor transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise,without the prior permission of the publisherCover design and layout by anu PressPrinted by griffin PressThis edition C 2015 ANU eViewContentsAbstractAcknowledgementsPreface○ verviewhapter I: Bayesian Basics Part IIntroduction1. 2 Bayes rule1.3 Bayes factors4 Bayesian models1.5 The posterior distribution1. 6 The proportionality formula1. 7 Continuous parameters1. 8 Finite and infinite population inferenceL9 Continuous data1. 10 Conjugacy24I I Bayesian point estimation1. 12 Bayesian interval estimation261. 3 Inference on functions of the model parameter1. 4 Credibility estimatesChapter 2: Bayesian Basics Part 262.1 Frequentist characteristics of bayesian estimators2.2 Mixture prior distributions2.3 Dealing with a priori ignorance802.4 The jeffreys prior2.5 Bayesian decision theory862.6 The posterior expected loss2.7 The Bayes estimateptern Basics part 33.1 Inference given functions of the data1093.2 Bayesian predictive inference3.3 Posterior predicti1303.4 Bayesian models with multiple parameters135Chapter 4: Computational Tools4.1 Solving equations1534.2 The Newton-Raphson algorithm4.3 The multivariate Newton-Raphson algorithm...,|64.4 The Expectation-Maximisation(EM) algorithm4.5 Variants of the nr and em algorithms1754.6 Integration techniques1884.7 The optimO functionChapter 5: Monte Carlo Basics205.1 Introduction5.2 The method of Monte Carlo integration for estimating mear5.3 Other uses of the mc sample2054 Importance samplin2095.5 MC estimation involving two or more random variables2|35.6 The method of composition..2|45.7 Monte Carlo estimation of a binomial parameter2|65.8 Random number generation2275.9 Sampling from an arbitrary discrete distribution2285.10 The inversion technique5. Random number generation via compositions2345.12 Rejection sampling5.13 Methods based on the rejection algorithm2405.14 Monte Carlo methods in Bayesian inference245.15 MC predictive inference via the method of composition25|5.16 Rao-Blackwell methods for estimation and prediction5.17 MC estimation of posterior predictive p-values258Chapter 6: MCMC Methods Part I2636.1 Introd6.2 The Metropolis algorithm2636.3 The batch means method2746.4 Computational issues2856.5 Non-symmetric drivers and the general Metropolis algorithm2866.6 The Metropolis-Hastings algorithm2906.7 Independence drivers and block sampling3056.8 Gibbs steps and the Gibbs samplerChapter 7: MCMC Methods Part 2..32troduction7.2 Data augmentation32Chapter 8: Inference via WinBUGS8troduction to b∪GS8.2 A first tutorial in bugs3678.3 Tutorial on calling BUGS in R89Chapter 9: Bayesian Finite Population Theory9. Introduction4079.2 Finite population notation and terminology4089.3 Bayesian finite population models9.4 Two types of sampling mechanism49.5 Two types of inference4129.6 Analytic inference4|39.7 Descriptive inference4|4Chapter 10: Normal Finite Population Models.46710. The basic normal-normal finite population model46710.2 The general normal-normal finite population model4770.3 Derivation of the predictive distribution of the nonsample vector4800.4 Alternative formulae for the predictive distribution of the nonsample vector480.5 Prediction of the finite population mean and other linear combinations .. 48310.6 Special cases including ratio estimation48410.7 The normal-normal-gamma finite population model49410.8 Special cases of the normal-normal-gamma finite population model49710.9 The case of an informative prior on the regression parameter50hapter |I: Transformations and Other Topicsference on complicated quantities2 Data transformations52611.3 Frequentist properties of Bayesian finite population estimators536Chapter 12: Biased Sampling and Nonresponse.5592.1 Review of sampling mechanisms12.2 Nonresponse mechanisms..5602.3 Selection bias in volunteer surveys57812.4 A classical model for self-selection bias5782.5 Uncertainty regarding the sampling mechanism58312.6 Finite population inference under selection bias in volunteer surveys588Appendix A: Additional ExercisesExercise A I Practice with the metropolis algorithm609Exercise A 2 Practice with the mh algorithmExercise A 3 Practice with a Bayesian finite population regression model626Exercise A 4 Case study in Bayesian finite population modelswith biased sampling638Appendix B: Distributions and Notation667B. The normal distributionB.2 The gamma distribution68B.3 The exponential distribution669B. 4 The chi-squared distribution669B.5 The inverse gamma distribution670B. 6 The t distribution670B. 7 The f distributionB.8 The(continuous)uniform distributionB. 9 The discrete uniform distribution6666B io The binomial distributionB. The bernoulli distribution672B 12 The geometric distribution672Appendix C: Abbreviations and AcronymsBibliography677Abstract