Zen and the Art of Bayesian Analysis


C. Pozrikidis


Chester & Bennington

374 pages including covers

Download the first version 26.01 (zaba_26.1.pdf)

Please forgive typographical, conceptual, and other errors. The book should still be readable, mostly accurate, and should fulfil its intended role. Further revisions will correct these errors.

Remember: "It's not the size of the dog in the fight, it's the size of fight in the dog."

What is this?

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 against 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 wheelchair.

You are a frog in a pond and you sense in your toes that your friend, Funny Fins, is approaching. 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 Bayess' theorem, elementary concepts from statistics and mathematics are required. To understand the consequences of the the- orem, an open mind full, creativity, and willingness to think instead of accepting is required. The former is explained and the latter is encouraged in this book.

One mental block in applying Bayes' theorem is that forward and backward reasoning must be simultaneously exercised. 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? Once this mental block has been overcome, the rest is easy. Deductions and inferences based on Bayesian analysis range from useful, to thought provoking, to profound.

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, professionals, 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 de- sired 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. Narratives in the form of commentary and short stories are inter- spersed in the book. The selection of the narratives is guided by a prime directive that is consistent with the Bayesian approach: inner goodness amounts to developing an internal prism that projects the rays of fairness onto the subconsciousness, while rejecting the harmful components. Bayes' theorem allows us to anticipate, estimate, and then reject the harmful components, preferably in foresight and hope- fully in hindsight. All short stories included in this books are real.

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. You never really know what kind of trauma people carry inside them.

Random acts of kindness

If you enjoyed reading this book, please consider performing a random act of kindness, saying a prayer for the author, saying another prayer for the pretender, or donating what you can afford to the St. Jude Children's Research Hospital in Memphis, Tennessee. Please be kind to one another, you never know what kind of trauma lies behind the smile. Fly high in Heaven Robin and Chester.