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

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.

References in corpus (1)

• Stationary max-stable fields associated to negative definite functions

Cited by in corpus (10)

• Statistical Modeling of Spatial Extremes
• A hierarchical max-stable spatial model for extreme precipitation
• Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain
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• Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process
• Calibration of conditional composite likelihood for Bayesian inference on Gibbs random fields
• Spatial extremal modelling: A case study on the interplay between margins and dependence
• A composite likelihood approach to computer model calibration using high-dimensional spatial data
• Discussion of "Statistical Modeling of Spatial Extremes" by A. C. Davison, S. A. Padoan and M. Ribatet