Introduction to Bayesian Statistics, 2nd Edition [Hardcover]

William M. Bolstad (Author)

Book Description

Publication Date: August 15, 2007 | ISBN-10: 0470141158 | ISBN-13: 978-0470141151 | Edition: 2nd

Praise for the First Edition

"I cannot think of a better book for teachers of introductory statistics who want a readable and pedagogically sound text to introduce Bayesian statistics."
—Statistics in Medical Research

"[This book] is written in a lucid conversational style, which is so rare in mathematical writings. It does an excellent job of presenting Bayesian statistics as a perfectly reasonable approach to elementary problems in statistics."
—STATS: The Magazine for Students of Statistics, American Statistical Association

"Bolstad offers clear explanations of every concept and method making the book accessible and valuable to undergraduate and graduate students alike."
—Journal of Applied Statistics

The use of Bayesian methods in applied statistical analysis has become increasingly popular, yet most introductory statistics texts continue to only present the subject using frequentist methods. Introduction to Bayesian Statistics, Second Edition focuses on Bayesian methods that can be used for inference, and it also addresses how these methods compare favorably with frequentist alternatives. Teaching statistics from the Bayesian perspective allows for direct probability statements about parameters, and this approach is now more relevant than ever due to computer programs that allow practitioners to work on problems that contain many parameters.

This book uniquely covers the topics typically found in an introductory statistics book—but from a Bayesian perspective—giving readers an advantage as they enter fields where statistics is used. This Second Edition provides:

• Extended coverage of Poisson and Gamma distributions

• Two new chapters on Bayesian inference for Poisson observations and Bayesian inference for the standard deviation for normal observations

• A twenty-five percent increase in exercises with selected answers at the end of the book

• A calculus refresher appendix and a summary on the use of statistical tables

• New computer exercises that use R functions and Minitab® macros for Bayesian analysis and Monte Carlo simulations

Introduction to Bayesian Statistics, Second Edition is an invaluable textbook for advanced undergraduate and graduate-level statistics courses as well as a practical reference for statisticians who require a working knowledge of Bayesian statistics.

Editorial Reviews

Review

"The general tenor of this book is good and it should serve well as a text for an introductory statistics course taught from a Bayesian perspective." (Biometrics, September 2008)

"Like the first 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. (Technometrics, November 2008)

"Like the first 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." (Technometrics, November 2008)

"Highly recommended. Upper-division undergraduates; graduate students; professionals." (CHOICE, April 2008)

From the Back Cover

Praise for the First Edition

"I cannot think of a better book for teachers of introductory statistics who want a readable and pedagogically sound text to introduce Bayesian statistics."
—Statistics in Medical Research

"[This book] is written in a lucid conversational style, which is so rare in mathematical writings. It does an excellent job of presenting Bayesian statistics as a perfectly reasonable approach to elementary problems in statistics."
—STATS: The Magazine for Students of Statistics, American Statistical Association

"Bolstad offers clear explanations of every concept and method making the book accessible and valuable to undergraduate and graduate students alike."
—Journal of Applied Statistics

The use of Bayesian methods in applied statistical analysis has become increasingly popular, yet most introductory statistics texts continue to only present the subject using frequentist methods. Introduction to Bayesian Statistics, Second Edition focuses on Bayesian methods that can be used for inference, and it also addresses how these methods compare favorably with frequentist alternatives. Teaching statistics from the Bayesian perspective allows for direct probability statements about parameters, and this approach is now more relevant than ever due to computer programs that allow practitioners to work on problems that contain many parameters.

This book uniquely covers the topics typically found in an introductory statistics book—but from a Bayesian perspective—giving readers an advantage as they enter fields where statistics is used. This Second Edition provides:

• Extended coverage of Poisson and Gamma distributions

• Two new chapters on Bayesian inference for Poisson observations and Bayesian inference for the standard deviation for normal observations

• A twenty-five percent increase in exercises with selected answers at the end of the book

• A calculus refresher appendix and a summary on the use of statistical tables

• New computer exercises that use R functions and Minitab® macros for Bayesian analysis and Monte Carlo simulations

Introduction to Bayesian Statistics, Second Edition is an invaluable textbook for advanced undergraduate and graduate-level statistics courses as well as a practical reference for statisticians who require a working knowledge of Bayesian statistics.

See all Editorial Reviews

Product Details

• Hardcover: 464 pages
• Publisher: Wiley-Interscience; 2nd edition (August 15, 2007)
• Language: English
• ISBN-10: 0470141158
• ISBN-13: 978-0470141151
• Product Dimensions: 6.2 x 1.1 x 9.5 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars  See all reviews (14 customer reviews)
• Amazon Best Sellers Rank: #62,183 in Books (See Top 100 in Books)
  • #31 in Books > Medical Books > Basic Sciences > Biostatistics

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Most Helpful Customer Reviews

123 of 127 people found the following review helpful

4.0 out of 5 stars I learned a great deal about how the Bayesians do statistics May 24, 2004

By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE™ VOICE

Format:Hardcover

Approximately ten years ago, I received my initial statistics instruction from Dr. Robert Hogg, one of the leading educators in the field. There were occasions in class when he referred to the Bayesians, calling them a group of statisticians who rely on separate "a priori" and "a posteriori" analyses. As was his style, he made several jokes about "a posteriori" data. The structure of the class was such that he could not spend a great deal of time on Bayesian statistics, but his brief comments have always remained in my mind.
Therefore, when I received this book I immediately decided that I would read it. From it, I learned that the Bayesian approach to statistics is valuable and more accurately reflects the way humans think about the world. There are two primary philosophical approaches to statistics, the frequentist and Bayesian, with the frequentist being that most widely covered in basic statistics classes. A frequentist statistician uses random samples to provide estimates for unknown parameters of populations.
The Bayesian approach considers the population parameters to be random variables. The process of determining the value of a parameter starts with a subjective prior distribution of the parameter before the data is analyzed. After the data is collected and organized, Bayes' theorem is then used to revise your beliefs about the values of the parameters.
The first sections deal with the basics of summarizing and displaying data; logic, probability and uncertainty. These sections are generally not different from frequentist statistics, so there is no distinction between the Bayesian and frequentist philosophies. The first real differences occur at the end of chapter 5, which covers logic, probability and uncertainty. This is the point where Bayes' theorem is introduced and the principles of prior and posterior probabilities. Chapter 5 describes discrete random variables, and again, this section is standard material on probability.
The true philosophy of Bayesian statistics appears in chapter 6, which covers Bayesian inference for discrete random variables. As a newcomer to this area, I read it with great interest and learned a great deal about how Bayesian operations are performed. The remaining sections deal with the processes of performing basic statistical operations using Bayesian methods. This includes:

* Bayesian inference for binomial proportion.
* Bayesian inference for normal mean.
* Bayesian inference for difference between means.
* Bayesian inference for simple linear regression.

There are also two chapters that compare the Bayesian and frequentist techniques. Chapter 9 compares the Bayesian and fequentist techniques for the inference for proportions and chapter 11 compares the techniques for the inference for means. Exercises are included at the end of each chapter and appendix F is devoted to the answers to odd-numbered exercises.
I learned an enormous amount about Bayesian methods from this book and I strongly recommend it if you are interested in learned how the Bayesians do things.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

45 of 46 people found the following review helpful

5.0 out of 5 stars A Great Foundation for Learning Bayesian Statistics August 23, 2007

By David Ciemiewicz

Format:Hardcover|Amazon Verified Purchase

For people who need a primer in Statistics, especially Bayesian Statistics, I'd recommend this book.

When you are finished with this book, you can apply basic Bayesian methods for common case scenarios involving Normal distributions and Binomial distributions. Pragmatic scenarios for understanding how to interpret the results and understand when your prior may be inappropriate for your data were quite welcome and missing or underrepresented in other books and seminars I've taken in Bayesian statistics.

I especially appreciated the discussions on how to perform hypothesis tests in a Bayesian framework that is rare to find.

Bolstad does an excellent job in showing the relationship between Bayesian and Frequentist methods but, in my opinion, doesn't do enough exclamation points in the cases where he shows that they mathematically converge.

What is especially GOOD about this book is the fact that it DOESN'T get into the heavy mathematical underpinnings, history, and rationale for Frequentist vs Bayesian approaches. I have taken several seminars and read several books which focus on this approach of introducing rigorous mathematical formalism and integration using Markov Chain Monte Carlo (MCMC) was left somewhat bewildered by it. The PhD's who worked with me and tried to explain why Bayesian methods were better utterly failed because they overemphasized the high-falutin' mathematical rigor In fact, I would go so far as to say that the university professors and statisticians who emphasize these techniques are actually holding back the advancement and use of Bayesian methods by the general practicioners because of this. The average person doing statistics is going to do it by rote (whether we like it or not) so providing accessible methods to people who can do this is the way to further the cause.

Bolstad's book is a great foundation because it doesn't try to be comprehensive and mathematically rigorous book. It focuses on providing just enough mathematical underpinnings to understand the basic concepts and make progress without dwelling on it.

It would be great if Bolstad's book were used in high schools or in freshman college and university courses to introduce statistics. We'd convert more people to Bayesian methods if we did.

23 of 23 people found the following review helpful

5.0 out of 5 stars Intro to Bayesian Bolstad December 24, 2006

By George C. Newman

Format:Hardcover|Amazon Verified Purchase

This is an outstanding introduction for anyone with a modest knowledge of algebra. It includes some of the clearest expositions of fundamental statistical concepts and then extends and re-interprets those concepts in a way that makes Bayesian logic natural and intuitive. Excellent problems to solve illustrating and solidifying the concepts of each chapter. First rate reading!