A Discrepancy Measure Based on Expected Posterior Probability

Resumen

Two prior predictive distributions f(x) and g(x) are associated with two equally plausible models Mf and Mg, respectively. A single observation x from f(x) would update the probability of Mf from 1/2 to f(x) /[f(x) + g(x)]. The discrepancy D_EP(f || g) between distributions f(x) and g(x) equals E[p(Mf|xf)], that is, the expected posterior probability for Mf after a single observation x from f(x). In contrast to the Kullback-Leibler discrepancy (which is based on the expected logarithm of the Bayes factor for Mf) the discrepancy D_EP(f || g) (a) is symmetric in the sense that D_EP(f || g) = D_EP(g || f); (b) is defined even when the two distributions are not absolutely continuous with respect to one another; (c) is robust to differences in the tail of the distributions; and (d) quantifies dissimilarity of distributions on the familiar scale of probability. For hypothesis testing, this implies that the expected posterior probability for a true null hypothesis H0 equals the expected posterior probability for a true alternative hypothesis H1, despite the fact that default Bayes factors generally accumulate much more quickly for a true H1 than they do for a true H0.

Áreas y palabras clave

Cómo citar (APA 7)

Wagenmakers, E. J. (2025). A Discrepancy Measure Based on Expected Posterior Probability. https://doi.org/10.31234/osf.io/2ky5p_v1