Bayesian inference for interpretation of polygraph results in the courtroom

The Psychophysiological Detection of Deception, or 'polygraph' test as it is commonly known, is often used in screening of applicants for employment in security or information-sensitive positions, in law enforcement, and in the courtroom. In the courtroom, the primary use of the polygraph is by the criminal defence team to bolster belief in the innocence of the defendant. In publications and in testimony, professional polygraphers present polygraph 'accuracy' as some combination of sensitivity and specificity. They rarely describe the positive and negative predictive value of the test (PPV and NPV, respectively) or place confidence limits on estimates for these measures. Thus, courts and juries are confronted with the difficult problem of assessing the evidentiary value of the polygraph as compared to other evidence. Despite more than 80 years of field use, there is very limited data that may be applied to assess the diagnostic utility of the polygraph for purposes of establishing the innocence of a defendant. In this article, we present a fully Bayesian analysis of what is probably the largest and most realistic existing data set and we obtain the posterior distribution for the PPV(the probability of guilt conditioned on 'failing' the polygraph) and the NPV (the probability of innocence conditioned on 'passing' the polygraph). We show that these quantities have a high degree of uncertainty that is often unexpressed when just point estimates are given. This information may be of value to courts and juries weighing the contribution of polygraph evidence.