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

Morro Bay, California

Richard Wollert

Vancouver, Washington, rwwollert{at}aol.com

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.

Key Words: sexually violent predators • actuarial assessment • Bayes's Theorem • civil commitment • null hypothesis

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