Joint Posterior Inference for Latent Gaussian Models with R-INLA

TL;DR

This paper advances Bayesian inference for Latent Gaussian Models by developing methods within R-INLA to approximate joint posteriors, including skewness corrections, improving over traditional univariate approaches.

Contribution

It introduces a new framework for joint posterior approximation in Latent Gaussian Models within R-INLA, incorporating Gaussian copula structures and skewness adjustments.

Findings

Joint approximations inherit Gaussian copula structure

Methods provide skewness corrections for better accuracy

Sampling procedures are adjusted for skewness

Abstract

Efficient Bayesian inference remains a computational challenge in hierarchical models. Simulation-based approaches such as Markov Chain Monte Carlo methods are still popular but have a large computational cost. When dealing with the large class of Latent Gaussian Models, the INLA methodology embedded in the R-INLA software provides accurate Bayesian inference by computing deterministic mixture representation to approximate the joint posterior, from which marginals are computed. The INLA approach has from the beginning been targeting to approximate univariate posteriors. In this paper we lay out the development foundation of the tools for also providing joint approximations for subsets of the latent field. These approximations inherit Gaussian copula structure and additionally provide corrections for skewness. The same idea is carried forward also to sampling from the mixture representation, which we now can adjust for skewness.