A note on the Bayes factor for small interval hypotheses

Abstract

For the outcomes of multiple independent populations, a small interval hypothesis states that the maximum value of the parameters that determine the outcomes is no more than a small distance apart from the minimum value. An explicit expression is given for the probability of this hypothesis, from which related Bayes factors are obtained. Examples are given for how to obtain these Bayes factors for the ‘about equal’ hypothesis.

Keywords:

• Bayes factor
• small interval hypothesis

Acknowledgments

The author thanks the editor and the anonymous reviewer for their valuable comments and suggestions.