Review: Doing Bayesian Data Analysis

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Bayes Theorem

Bayesian Statistics is a field of statistics based upon probabilities, or how much you believe a hypothesis. As a simple example, consider a subject who has tested positive for drugs. Should a positive test immediately imply guilt? Take into consideration the following: each test has a false positive/negative rate, and each group (in this case drug and non-drug users) has a particular true rate of occurrence. Bayesian statistics can factor these values into account, and rather than resulting in a boolean, yes/no answer, it results in a belief as to whether the subject is a drug user. Consider a test that is 99% accurate - it will indicate true or false values 99% of the time. If 0.5% of the population are uses of that drug, a positive test - based upon bayesian statistics and Bayes' Rule - calculates the probability that the subject has a 33% chance of being a user - a vastly different conclusion than being immediately labelled guilty.

The example above is a simple case of applying Bayesian statistics - yet it can get much more complex. Doing Bayesian Data Analysis by John Krusche is an introductory textbook about the simple and more complex theory and applications of Bayesian statistics. The book is broken down into three parts. Part 1 introduces the basics - probability theory and Bayes' rule. Part 2 introduces the fundamentals, from Gibbs sampling to hierarchical modelling. Part 3 moves onto more complex concepts as Bayesian data analysis applies to the Generalized Linear Model.

Doing Bayesian Data Analysis is quite possibly one the best book I've seen with respect to Bayesian statistics - in fact this textbook is up there with some of the best I have read in any field. What sets this book apart from the rest? In my opinion many textbooks lay down concepts, theory, symbols, and equations: great when serving as a reference, but sometimes difficult to come away with knowledge on how to apply what you've learned. Doing Bayesian Data Analysis leans more towards example, simplicity, and exercises - all presented in a clear and concise manner. In affect - this book teaches, and does so in a remarkable way. For example, chapter 4 presents a derivation of Bayes' rule, which is often explained in conditional probability equations littered with symbols of probability (as an example look at the current Wikipedia page1). Doing Bayesian Data Analysis breaks the derivation out into 4 pages, first doing so mathematically, then through example (using the simple but effective example of coin flipping). After reading this chapter, and perhaps for the first time, I felt I understood the power and intuition behind Bayes' rule. The book continually presents subjects in forms capable of being read by the expert and layperson alike - I came away from this book with the ability to immediately apply concepts such as Bayesian Linear Regression in my research.

Doing Bayesian Data Analysis is an excellent textbook for an upper level undergraduate, graduate student, or researcher. The book could be used as a course textbook, but is also clear enough that it can be followed on one's own (the route I chose). The author provides an overview of prerequisites in the intro - previews of which may be available online. Briefly, one should have a good understanding of statistics, math, and some calculus - an expert's grasp of these subjects is not required. Further, while not required, knowing some programming or R will help in being able to work through the code examples and questions.

Don't let the dogs on the cover fool you into thinking this book is anything less than it truly is - currently one of the best Bayesian statistics textbooks available.

1As of July, 2013

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