Bayesian detection with the posterior distribution of the likelihood ratio

This paper focuses on simple versus composite hypothesis testing in Bayesian settings. The Posterior distribution of the Likelihood Ratio (PLR) provides an interesting alternative to the classical Bayes Factor (BF). First its general properties are studied and reveal its relationships with the BF, the Fractional BF and the Generalized Likelihood Ratio. Then the PLR is proved to be equal to a frequentist p-value for an invariant model and the corresponding invariant prior. A practical implementation of the test can be performed using a simple Monte Carlo Markov Chain. Performances of the PLR used as a test are illustrated on extra-solar planet detection using direct imaging. Finally, the possibility to use different parametrizations of the test is illustrated by the study of their operating characteristics.