## Bayes 7: sensitivity and specificity

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

Happy Monday, fellow Bayesians! In this blog post, I will introduce and formally define the technical concepts of ‘sensitivity’ and ‘specificity.’ In the context of my Bayesian model of the litigation game, these concepts refer to the underlying reliability of a civil or criminal trial to distinguish between guilty and innocent defendants as follows:

1. Sensitivity. For starters, the ‘sensitivity’ of the litigation game—written as Pr(B|A) or, in our model, Pr(+|guilty)—indicates how well a civil or criminal trial is able to correctly impose liability on guilty defendants. In summary, this measure is defined formally as the probability of a positive litigation outcome (i.e., liability imposed on the defendant, which represents a ‘positive’ outcome from the plaintiff’s or prosecutor’s perspective), given that the defendant being tried has actually committed an unlawful wrongful act
2. Specificity. By contrast, the ‘specificity’ of the litigation game, which may be written as Pr(–|innocent), reflects how well a civil or criminal trial is able to correctly screen out innocent defendants. This measure is defined formally as the probability of a negative litigation outcome (i.e., no liability imposed on the defendant, which represents a ‘negative’ outcome from the perspective of the moving party, plaintiff or prosecutor), given that the defendant has not committed a wrongful act.

The bottom line is this: Sensitivity and specificity are crucial concepts because civil or criminal liability should be imposed only on guilty defendants, i.e., defendants who have in fact committed an unlawful or wrongful act. In my next post, I will make three general points about Bayesian reasoning, and in my next few posts after that, I will present my Bayesian model of litigation outcomes.