Bayes Factors for Peri-Null Hypotheses

Understand

A perennial objection against Bayes factor point-null hypothesis tests is that the point-null hypothesis is known to be false from the outset.

• We examine the consequences of approximating the sharp point-null hypothesis by a hazy `peri-null' hypothesis instantiated as a narrow prior distribution centered on the point of interest.
• The peri-null Bayes factor then equals the point-null Bayes factor multiplied by a correction term which is itself a Bayes factor.
• For moderate sample sizes, the correction term is relatively inconsequential; however, for large sample sizes the correction term becomes influential and causes the peri-null Bayes factor to be inconsistent and approach a limit that depends on the ratio of prior ordinates evaluated at the maximum likelihood estimate.