Bayesian Thought: Introduction


“Reality is that which, when you stop believing in it, doesn’t go away”.
How to Build a Universe That Doesn’t Fall Apart Two Days Later, Philip K. Dick


I have been considering the power of belief since the tragic days of September 2001. Belief shapes the goals we choose to pursue and the actions we will take in their pursuit. In a vaguely understood process, the thoughts we entertain affect the formation of our beliefs. Just how much power our choices of thought and action have to establish or change our beliefs is a difficult, but important question to ask. I invite you to join me in exploring this question. Whatever answers we are able to find have very practical consequences for each of us as individuals and for our societies.

In my research I came across Bayesian mathematics as a model dealing directly with the relationship between reason and belief. Approaching the subject with these questions, I found a conceptual framework offering a coherent world view larger than any particular mathematical technique. The whole fabric of Bayesian thought concerns itself with human knowledge and the beliefs that arise as we reason about our knowledge under the conditions of ubiquitous uncertainty. It recognizes explicitly the inescapable limitations that constrain inductive propositions; that induction can only result in statements of plausibility. Using the conceptual tools of Bayesian thought, a rough outline of a philosophy began to emerge, a philosophy by no means wholly new but one so at odds with the prevailing notions that few people have had the chance to encounter it. The position is characterized by an insistence on conditional probability as a critically important lens through which to ponder our place in the world. The probabilist historically is a mathematician who studies probability theory; I will argue that this theory has reached such profound development it is time to extend that definition. A probabilist in my view is an adherent to a coherent, defensible philosophic position available to guide mathematicians and everyman alike.

I found myself wanting to read a book that used the Bayesian position as a filter through which to examine these important issues and in my research I uncovered many very interesting authors and much fascinating work. However, I found that this material is almost wholly presented in mathematical textbooks, dense upper-graduate mathematical textbooks and scientific papers. There are a few non-mathematical books exploring how the Bayesian position can be used to justify the scientific method or epistemology, but these too have a narrowly targeted audience of academic philosophers. Few people put such textbooks high on their list of pleasure reading. The subject has not received a popular science treatment that I was able to find except one volume which focused on causal models, an important part of the Bayesian picture but just one part (Slomon 2005). During the writing of this book a second work for a popular audience appeared providing a look into the rocky history of the use of Bayes theorem, ‘The Theory That Would Not Die’ (Mcgrayne 2011). What has not been made available is a presentation of just what Bayesian thought is as it interprets probability as logic. I set out to rectify this oversight, to share this idea and use it as a philosophic tool for exploring reason and belief. In ‘Resurrecting Logical Probability’ J. Franklin (2001) observes that “logical probabilists have almost disappeared from the face of the earth”. Gratefully, as we will see, this is not the case. In the last twenty years, since the development of Gibbs sampling and Monte Carlo Markov Chains, there has been a quiet revolution in a wide variety of research fields as Bayesian techniques infiltrated one scientific and engineering discipline after the other, providing solutions to problems that were previously intractable.

Probability is typically thought of as being concerned with games of chance involving dice, coins, and cards and drawing balls from urns. From this view it is irrelevant to the important work of adults solving real world issues using less than perfect theories and what is often ambiguous data. This is a crippling, dated conception of probability, restricting its applicability to so-called random variables. In the larger, historical conception of probability it makes sense to assign probabilities to propositions. By returning to the roots of probability theory and taking as its example Laplace’s presentation in ‘A Philosophical Essay on Probabilities’ (Laplace 1951) this work seeks to explain how the results of plausible reasoning apply to real life. It explores belief from its most primitive expression as a descriptor for the behavior of a paramecium to the most abstract forms encountered in human psychology. The central thesis is that beliefs are a fundamental adaptation to uncertain environments and because they are so fundamental choosing to assent in a belief influences much more about one’s entire life experience then is typically acknowledged. The reason for writing is to illustrate the central concept of Bayesian thought, that it is logically coherent to entertain degrees of belief. This removes the cognitive straightjacket that insists on classifying all beliefs as either true or false, replacing this black and white thinking with a nuanced understanding more adaptive for dealing with life in the information age. Probabilists hope that by spreading this important idea it will act as a leaven to the fractious rhetoric that has poisoned our public discourse and aid us in making difficult, critical decisions. More directly it is my hope that those who join me on this journey will acquire a practical thinking skill, a useful addition to your cognitive tool belt.

It has been said that encountering Bayesian thought is almost like a religious experience. Maybe. I found it capable of organizing and aiding my understanding of a number of seemingly unrelated areas, from emotional well being to interpreting the latest scientific discoveries. It has brought a conceptual coherence to my world view, logically defensible throughout while remaining deeply humanistic. Am I a convert? Let me put it this way: I do believe it is highly plausible that you too will derive real benefit from an acquaintance with this idea, one of the most fundamental and fascinating achievements of the human mind.

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