A Mathematical Proof and Example That Bayes's Theorem Is Fundamental to Actuarial Estimates of Sexual Recidivism Risk

Abstract

Expert witnesses in sexually violent predator (SVP) cases often rely on actuarial instruments to make risk determinations. Many questions surround their use, however. Bayes's Theorem holds much promise for addressing these questions. Some experts nonetheless claim that Bayesian analyses are inadmissible in SVP cases because they are not accepted by the relevant scientific community. This position is illogical because Bayes's Theorem is simply a probabilistic restatement of the way that frequency data are combined to arrive at whatever recidivism rates are paired with each test score in an actuarial table. This article presents a mathematical proof and example validating this assertion. The advantages and implications of a logic model that combines Bayes's Theorem and the null hypothesis are also discussed.

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“…It is thus most straightforward to address the problematic issues on the specific turf where they arise. For purposes more general than this paper, a Bayesian perspective has much to offer; see, e.g., Donaldson and Wollert 2008, Scurich and John 2012, and Harris and Rice 2013 Section 2.1 describes HMC's Table 1 of recidivism proportions and associated intervals for nine risk strata, and the conclusions HMC draw from them. The technical bases of frequentist probabilistic risk prediction (Section 2.2) and statistical intervals (Section 2.3) are then described and related to such data in a tutorial, non-mathematical style.…”