Introduction to Bayesian Statistics

**"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods."** There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. __Introduction to Bayesian Statistics, Third Edition__ also features: * Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior * The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods * Exercises throughout the book that have been updated to reflect new applications and the latest software applications * Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website __Introduction to Bayesian Statistics, Third Edition__ is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics. "' ... This edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods.' There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features:>> Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior>> The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods>> Exercises throughout the book that have been updated to reflect new applications and the latest software applications>> Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website. Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics."--Publisher's description Cover......Page 1 Contents......Page 7 Preface......Page 13 1 Introduction to Statistical Science......Page 17 2 Scientific Data Gathering......Page 29 3 Displaying and Summarizing Data......Page 47 4 Logic, Probability, and Uncertainty......Page 75 5 Discrete Random Variables......Page 99 6 Bayesian Inference for Discrete Random Variables......Page 125 7 Continuous Random Variables......Page 145 8 Bayesian Inference for Binomial Proportion......Page 165 9 Comparing Bayesian and Frequentist Inferences for Proportion......Page 185 10 Bayesian Inference for Poisson......Page 209 11 Bayesian Inference for Normal Mean......Page 227 12 Comparing Bayesian and Frequentist Inferences for Mean......Page 253 13 Bayesian Inference for Difference Between Means......Page 271 14 Bayesian Inference for Simple Linear Regression......Page 299 15 Bayesian Inference for Standard Deviation......Page 331 16 Robust Bayesian Methods......Page 353 17 Bayesian Inference for Normal with Unkown Mean and Variance......Page 371 18 Bayesian Inference for Mulrivariate Normal Mean Vector......Page 409 19 Bayesian Inference for the Multiple Linear Regression Model......Page 427 20 Computational Bayesian Statistics Including Markov Chain Monte Carlo......Page 447 A Introduction to Calculus......Page 493 B Use of Statistical Tables......Page 513 C Using the Included Minitab Macros......Page 539 D Using the Included R Functions......Page 559 E Answers to Selected Exercises......Page 581 References......Page 607 Index......Page 611