How to Make a Decision Based on the Minimum Bayes Factor (MBF): Explanation of the Jeffreys Scale

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Nguyen Duc Trung, Banking University HCMCFollow

Publication Date

7-2019

Comments

Technical Report: UTEP-CS-19-71

Abstract

In many practical situations, we need to select a model based on the data. It is, at present, practically a consensus that the traditional p-value-based techniques for such selection often do not lead to adequate results. One of the most widely used alternative model selection techniques is the Minimum Bayes Factor (MBF) approach, in which a model is preferred if the corresponding Bayes factor -- the ratio of likelihoods corresponding to this model and to the competing model -- is sufficiently large for all possible prior distributions. Based on the MBF values, we can decide how strong is the evidence in support of the selected model: weak, strong, very strong, or decisive. The corresponding strength levels are based on a heuristic scale proposed by Harold Jeffreys, one of the pioneers of the Bayes approach to statistics. In this paper, we propose a justification for this scale.