Introduction to Bayesian Statistics, 3rd Edition

“…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.

Table of Contents

Chapter 1 Introduction to Statistical Science
Chapter 2 Scientific Data Gathering
Chapter 3 Displaying and Summarizing Data
Chapter 4 Logic, Probability, and Uncertainty
Chapter 5 Discrete Random Variables
Chapter 6 Bayesian Inference for Discrete Random Variables
Chapter 7 Continuous Random Variables
Chapter 8 Bayesian Inference for Binomial Proportion
Chapter 9 Comparing Bayesian and Frequentist Inferences for Proportion
Chapter 10 Bayesian Inference for Poisson
Chapter 11 Bayesian Inference for Normal Mean
Chapter 12 Comparing Bayesian and Frequentist Inferences for Mean
Chapter 13 Bayesian Inference for Difference Between Means
Chapter 14 Bayesian Inference for Simple Linear Regression
Chapter 15 Bayesian Inference for Standard Deviation
Chapter 16 Robust Bayesian Methods
Chapter 17 Bayesian Inference for Normal with Unknown Mean and Variance
Chapter 18 Bayesian Inference for Multivariate Normal Mean Vector
Chapter 19 Bayesian Inference for the Multiple Linear Regression Model
Chapter 20 Computational Bayesian Statistics Including Markov Chain Monte Carlo
Appendix A Introduction to Calculus
Appendix B Use of Statistical Tables
Appendix C Using the Included Minitab Macros
Appendix D Using the Included R Functions
Appendix E Answers to Selected Exercises