## Bayes 4

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

I resume by Bayesian blog series by explaining why Bayesian methods are like a meta-test, a way of testing the reliability of one’s tests. How? By allowing us to update and test our priors of a given uncertain event–e.g., whether x has cancer; whether y is a spam message; whether z committed a crime or a tort. In the case of a legal trial, as my last example suggests, the Bayesian approach is a formal method for updating one’s prior beliefs about a defendant’s guilt or innocence. Put another way, Bayesian reasoning is a method for testing the reliability and accuracy of a legal trial: it is a way of testing legal tests.

But how is a legal trial like a test? People often assume that trials are, instead, a search for the truth. The problem with this truth-function interpretation of trials, however, is that truth itself is a probabilistic ideal, not an absolute one, especially when there are different versions or interpretations of the truth. Furthermore, from the perspective of a trial attorney and the litigating parties, a trial is just a risk-taking activity, a game whose main object is to “win,” regardless of truth. Metaphorically speaking, then, a legal trial is more like poker and less like science. Of course, it helps to have the truth on one’s side, but my point here is that having the truth on one’s side is neither a necessary nor sufficient condition for winning at trial–the ultimate goal of litigation from the perspective of the parties. To sum up, a legal trial is not a dispassionate or scientific search for truth; it is a bet or wager on which party’s story or version of the truth is more likely to be accepted as true.

More importantly, truth is a probabilistic concept, for there can be competing conceptions of the truth in any given case. That is why a legal trial can be compared to a test–a test of the evidence the parties offer in support of their competing versions of the truth. Thus, a legal trial is more like a medical test or a spam filter, but instead of testing for cancer, HIV, or spam, litigation simply tests the strength of the moving party’s case. In Anglo-American law, the moving party is either the government (e.g., the prosecution in a criminal case) or a private party (e.g., the plaintiff in a civil case), and when a prosecutor or plaintiff goes to trial, he is literally putting his allegations (his evidence) to the test. In either case, civil or criminal, the moving party must submit sufficient evidence to pass the relevant test. In civil cases the test is pass/fail–e.g., the preponderance of the evidence standard. In criminal ones the test is more demanding–e.g., the reasonable doubt standard. In either case, the question is the same: has the prosecution proven its case beyond a reasonable doubt? Or, has the plaintiff proven his case by a preponderance of the evidence? This, then, is what I mean when I describe a legal trial as a test.

With this background in mind, how can we use Bayesian methods to test our legal tests? I shall turn to this question in my next few blog posts.