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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.
Preface xiii
1 Introduction to Statistical Science 1
2 Scientic Data Gathering 13
3 Displaying and Summarizing Data 31
4 Logic, Probability, and Uncertainty 59
5 Discrete Random Variables 83
6 Bayesian Inference for Discrete Random Variables 109
7 Continuous Random Variables 129
8 Bayesian Inference for Binomial Proportion 149
9 Comparing Bayesian and Frequentist Inferences for Proportion 169
10 Bayesian Inference for Poisson 193
11 Bayesian Inference for Normal Mean 211
12 Comparing Bayesian and Frequentist Inferences for Mean 237
13 Bayesian Inference for Di erence Between Means 255
14 Bayesian Inference for Simple Linear Regression 283
15 Bayesian Inference for Standard Deviation 315
16 Robust Bayesian Methods 337
17 Bayesian Inference for Normal with Unknown Mean and Variance 355
18 Bayesian Inference for Multivariate Normal Mean Vector 393
19 Bayesian Inference for the Multiple Linear Regression Model 411
20 Computational Bayesian Statistics Including Markov Chain Monte Carlo 431
William M. Bolstad, PhD, is a retired Senior Lecturer in the Department of Statistics at The University of Waikato, New Zealand. Dr. Bolstad's research interests include Bayesian statistics, MCMC methods, recursive estimation techniques, multiprocess dynamic time series models, and forecasting. He is author of Understanding Computational Bayesian Statistics, also published by Wiley.
James M. Curran is a Professor of Statistics in the Department of Statistics at the University of Auckland, New Zealand. Professor Curran's research interests include the statistical interpretation of forensic evidence, statistical computing, experimental design, and Bayesian statistics. He is the author of two other books including Introduction to Data Analysis with R for Forensic Scientists, published by Taylor and Francis through its CRC brand.
