Zen and the Art of Bayesian Analysis

C. Pozrikidis



From the Preface

You walk into an expensive restaurant and ask a customer to reveal their degree of general happiness on a scale from zero to ten. Bayes' theorem will tell you how to estimate the annual income of that person, given some information on income v. happiness non-specific to the person. Zen will ask you not to be presumptuous about the person and wish them well, no matter how well off they are.

You want to rediscover yourself and you are thinking about taking a road trip. Bayes' theorem will tell you whether the trip will help, given some information non-specific to your current frame of mind. Zen will tell you that you can rediscover yourself and escape the unpleasant, the mundane, and the tedious in a prison cell.

You are a frog in a pond and you sense in your toes that your friend, Funny Fins, is swimming. Bayes' theorem will tell you how far Funny Fins is, and if she is moving toward you, given some generic analysis of fluid flow pertinent to swimming. Zen will tell you that there is always time for Bayesian analysis, but not enough time to spend with a dear friend, especially when the friend's name is groundhog Bilbo.

To apply Bayes' theorem, elementary concepts from statistics and mathematics are required. To understand the consequences of the theorem, an open mind full of possibilities, creativity, and willingness to think instead of accept is required. The former is explained and the latter are encouraged in this book.

One mental block in applying Bayes' theorem is that forward and backward reasoning must be simultaneously exercized. For example, we may consider a tomato plant that thrived and ask: how much was it watered? or we may water a tomato plant by a certain amount and ask: will it wither or thrive? A second mental block is the realization that only states corresponding to the same level of data or information can be meaningfully compared. Once these mental blocks have been overcome, the rest is easy. Deductions and inferences based on Bayesian analysis range from useful, to thought-pattern altering, to gratifying.

My two main goals in this book are to (a) introduce Bayes' theorem from a rigorous yet informal standpoint, and (b) discuss methods of Bayesian analysis in a broad range of applications and diverse settings. All necessary concepts are defined and introduced for a self-contained discourse; elementary background information from combinatorics is provided in an appendix.

This book is addressed to a diverse audience including teachers, professors, students, and anyone is interested in learning the essence of Bayesian analysis. Familiarity with high-school level mathematics is only required in most early sections, while college-level mathematics is required in more advanced sections. The reader may select the desired level of mathematical comfort and skip sections that appear too mathematical, without compromising the understanding of subsequent material.

Several Matlab codes performing computations, simulations, and visualization are listed for illustration.

By reading this book, you will learn what you already know. You approach a problem, situation, suggestion, concept with some idea; you get some data, input, measurements, observations or insights to test your idea; and then you get closer to the truth and revise your initial idea. Perhaps more important, by reading this book you will affirm that nothing occurs in vacuum, and that actions have short-term, long-term, predictable, and surprising consequences.

Errata and supplements