Abstract: This paper proposes and discusses the use of composite marginal likelihoods for Bayesian inference. This approach allows one to deal with complex statistical models in the Bayesian framework, when the full likelihood - and thus the full posterior distribution - is impractical to compute or even analytically unknown. The procedure is based on a suitable calibration of the composite likelihood that yields the right asymptotic properties for the posterior probability distribution. In this respect, an attractive technique is offered for important settings that at present are not easily tractable from a Bayesian perspective, such as, for instance, multivariate extreme value theory. Simulation studies and an application to multivariate extremes are analysed in detail.
Key words and phrases: Asymptotic theory, Bayesian inference, estimating equation, extreme value theory, pairwise likelihood, pseudo-likelihood.