This paper proposes and discusses the use of composite marginal like-
lihoods 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 un-
known. The procedure is based on a suitable calibration of the composite likelihood
that yields the right asymptotic properties for the posterior probability distribu-
tion. 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 in-
stance, multivariate extreme value theory. Simulation studies and an application
to multivariate extremes are analysed in detail
