Bayes factors for peri-null hypotheses

Abstract A perennial objection against Bayes factor point-null hypothesis tests is that the known to be false from outset. We examine consequences of approximating sharp by a hazy ‘peri-null’ instantiated as narrow prior distribution centered on point interest. The peri-null then equals multiplied correction term which itself factor. For moderate sample sizes, relatively inconsequential; however, for large becomes influential and causes inconsistent approach limit depends ratio ordinates evaluated at maximum likelihood estimate. characterize asymptotic behavior briefly discuss suggestions how construct are also consistent.