Bounds on Intrinsic Bayes Factors and Least Favorable Intrinsic Priors for General Statistical Hypothesis Testing

Abstract

Hypothesis Testing is the most contentious procedure in statistical Methodology. P values rejects Null Hypotheses far too easily, specially for large samples. On the other hand, Bayes Factors depends on assumptions, for example regarding Intrinsic Bayes Factors, which average? Arithmetic, Geometric, Median? Our bound is the infimum over all the averages. We develop a lower bound on Intrinsic Bayes Factors that adjust authomatically with the sample size. Furthermore, we introduce the new idea of {\it{\textbf{Least Favorable Intrinsic Prior}}}, which corresponds to the least favourable possible training samples. The bound sets a bridge between Intrinsic Bayes Factors and Adrian Smith and David Spiegelhalter methodology.