Improving the INLA approach for approximate Bayesian inference for latent Gaussian models

TL;DR

This paper presents a copula-based correction to improve the accuracy of INLA for Bayesian inference in latent Gaussian models, especially in challenging GLMM cases with low smoothing.

Contribution

A novel copula-based correction method for INLA that extends its applicability to more problematic GLMM scenarios, with minimal additional computational cost.

Findings

Correction improves INLA accuracy in extreme GLMM cases

Method performs well on real and simulated data

Implementation adds negligible computational overhead

Abstract

We introduce a new copula-based correction for generalized linear mixed models (GLMMs) within the integrated nested Laplace approximation (INLA) approach for approximate Bayesian inference for latent Gaussian models. While INLA is usually very accurate, some (rather extreme) cases of GLMMs with e.g. binomial or Poisson data have been seen to be problematic. Inaccuracies can occur when there is a very low degree of smoothing or "borrowing strength" within the model, and we have therefore developed a correction aiming to push the boundaries of the applicability of INLA. Our new correction has been implemented as part of the R-INLA package, and adds only negligible computational cost. Empirical evaluations on both real and simulated data indicate that the method works well.