Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes

TL;DR

This paper explores Bayesian inference using composite likelihoods, employing Metropolis-Hastings algorithms with adjustments, applied to spatial extremes data, bridging a gap in Bayesian methods for complex likelihoods.

Contribution

It introduces methodologies for Bayesian inference with composite likelihoods and evaluates their effectiveness through simulations and real spatial extremes data.

Findings

Adjusted algorithms improve approximation of the true posterior

Bayesian methods are feasible with composite likelihoods in spatial extremes

Performance varies with adjustment techniques and data complexity

Abstract

Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of the usual maximum likelihood estimator, Bayesian inference based on composite likelihoods has yet to be explored. In this paper we investigate the use of the Metropolis--Hastings algorithm to compute a pseudo-posterior distribution based on the composite likelihood. Two methodologies for adjusting the algorithm are presented and their performance on approximating the true posterior distribution is investigated using simulated data sets and real data on spatial extremes of rainfall.