On Bayes, part 3: all tests are imperfect

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

Tests are imperfect; that is, they sometimes detect things that do not exist (“false alarms” or false positives) and miss things that do exist (“misses” or false negatives). Consider spam filters, which are designed to detect unwanted email messages and reroute them into a separate spam or junk email folder. The problem is that no spam filter is perfect. Sometimes the spam net is cast too wide and some non-spam email messages fall into the spam filter and into one’s junk email folder; sometimes the spam net is not wide enough and spam messages get past the filter and into your regular inbox. (As an aside, I blogged about these so-called Type I and Type II errors, or the problem of false alarms and misses, four years ago here.)

By analogy, the same problem occurs in law and litigation. [1] Specifically, “frivolous” civil cases and criminal cases in which the prosecutor has “overcharged” the defendant can be compared to spam. In a perfect legal system, judges and juries would be able to detect and distinguish frivolous civil claims from valid ones as well as superfluous or trumped-up criminal charges from substantial ones. But judges and juries make mistakes. We all do. Sometimes, judges will dismiss valid claims (misses) and allow frivolous claims to go to trial (false alarms). Likewise, juries will occasionally convict innocent men (false alarms) or allow the guilty to go free (misses). I will further elaborate on this theme–on how legal trials are imperfects tests–in my next post.

Screen Shot 2021-03-02 at 11.35.05 AM

Image credit: @TheUSMLE

[1] See, e.g., Christoph Engel & Gerd Gigerenzer, “Law and Heuristics: An Interdisciplinary Venture,” in Engel & Gigerenzer, eds., Hueristics and the Law (2006), pp. 1-16, available here.

About F. E. Guerra-Pujol

When I’m not blogging, I am a business law professor at the University of Central Florida.
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1 Response to On Bayes, part 3: all tests are imperfect

  1. Pingback: Bayes 9: the model | prior probability

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