involves a ratio of marginal likelihoods, the so-called Bayes factor: which can be stated schematically as posterior odds = prior odds × Bayes factor See also Empirical Bayes methods Lindley's paradox Marginal probability Bayesian information criterion References Charles S. Bos. "A comparison of marginal likelihood computation methods". In W. Härdle and B. Ronz, editors, COMPSTAT 2002: Proceedings in Computational Statistics, pp. 111–117. 2002. (Available as a preprint on the web: ) de Carvalho, Miguel; Page, Garritt; Barney, Bradley (2019). "On the geometry of Bayesian inference". Bayesian Analysis. 14 (4): 1013‒1036. (Available as a preprint on the web: ) The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay. Bayesian statistics