Discussion paper: P-value likelihood ratios for evidence evaluation

Much debate exists between Frequentist and Bayesian methods in statistics. In the evaluation of evidence, the likelihood ratio is credited with quantifying the value of evidence in favour of one or other proposition by considering the probability of the evidence conditional on each proposition and this then converts the Bayesian prior odds into the posterior odds. Motivated by this approach, this paper considers an alternative p-value-based likelihood ratio by explicitly taking into account the behaviour of the Frequentist p-value under both hypotheses, rather than restricting focus solely on the null hypothesis. It is shown that by accommodating the alternative hypothesis, analysis leads to inferential conclusions which are consistent with Bayesian methods.