International Journal for Uncertainty Quantification

RELATIONSHIP BETWEEN BAYESIAN AND FREQUENTIST SIGNIFICANCE INDICES

ABSTRACT

The goal of this paper is to illustrate how two significance indicesthe frequentist p-value and Bayesian e-value have a straight mathematical relationship. We calculate these indices for standard statistical situations in which sharp null hypotheses are being tested. The p-value considered here is based on the likelihood ratio statistic. The existence of a functional relationship between these indices could surprise readers because they are computed in different spaces: p-values in the sample space and e-values in the parameter space.