The LGM Split Sampler: An Efficient MCMC Sampler for Latent Gaussian Models

• Activity Number: 302 - Bayesian Modeling
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Birgir Hrafnkelsson* and Dan Simpson and Oli Pall Geirsson
• Companies: University of Iceland and University of Bath and University of Iceland
• Keywords: latent Gaussian models ; Markov chain Monte Carlo ; Bayesian hierarchical models ; computational efficiency ; spatially varying scale parameter ; spatial extremes

Abstract

Latent Gaussian models (LGMs) form a flexible subclass of Bayesian hierarchical models and have become popular in many applications. Even though the LGM grew from achieving a good balance between generality and computational efficiency, the posterior inference becomes computationally challenging when a latent model is needed for the variance or scale of the data density function in addition to the latent model for the location parameter; or when the number of parameters associated with the latent model increases. To address these issues we propose a novel computationally efficient Markov chain Monte Carlo scheme: the LGM split sampler. The sampling scheme is designed to handle LGMs where latent models are imposed on more than just the mean structure of the likelihood; to scale well in terms of computational efficiency when the dimensions of the latent models increase; and to be applicable for any choice of a parametric data density function. To demonstrate the efficiency of the LGM sampler we apply it to spatial extremes that are modeled with spatially varying location and scale parameters.