## Bayes is not an oracle

Note: This is my first blog post in a month-long series on the basics of Bayesian probability theory.

It’s the “1st of tha month,” so as promised let’s begin my series of Bayesian blog posts, and let me start by stating “what Bayes is not.” It is not a magic conjurer, Delphic oracle, or “veritable sorcerer.” [1] That is, it is not a method for eliminating uncertainty. Instead, Bayesian probability is a method for measuring our level of uncertainty. [2] Put another way, the Bayesian approach to legal and moral judgements is not just a method of drawing inferences from observations or evidence presented; it is also a method of testing the strength or weakness of such inferences. This insight is extremely relevant to law and legal processes. Although Bayesian reasoning cannot replace human intuition or judgement or decide for us the ultimate guilt or innocence of a defendant, we can nevertheless use Bayesian methods to measure or evaluate the strength of a party’s evidence, whether it be evidence of guilt or evidence of innocence. As a result, Bayesian methods may not only be used offensively by a moving party (plaintiff or prosecutor) to measure the strength of his case; such methods can also be used defensively by a defendant to test or challenge the strength of the moving party’s case. (In my next post, I will show how legal trials are like bets.)

[1] People v. Collins, 438 P.2d 33, 33 (1968).

[2] See, e.g., Colin Howson &Peter Urbach, Bayesian Reasoning in Science, 350 Nature 371, 372 (1991) (Bayesian reasoning is a method of “characterizing a scientific conclusion about a hypothesis as a statement of its probability”); Stephen Fienberg & Mark Schervish, The Relevance of Bayesian Inference for the Presentation of Statistical Evidence and for Legal Decisionmaking, 66 Boston University Law Review 771, 773 (1986) (“Bayesian probability theory … provide[s] both a framework forquantifying uncertainty and methods for revising uncertainty measures in the light of acquired evidence”).