An Extended Simplified Laplace strategy for Approximate Bayesian inference of Latent Gaussian Models using R-INLA

TL;DR

This paper introduces an improved approximation method for Bayesian inference in Latent Gaussian Models, enhancing the accuracy of the Simplified Laplace strategy with minimal additional computational cost.

Contribution

The authors develop an extended approximation technique using the Extended Skew Normal distribution, improving accuracy over the existing SLA in R-INLA without significant computational overhead.

Findings

More accurate posterior density approximations achieved.

Enhanced method maintains computational efficiency.

Applicable to complex hierarchical models.

Abstract

Various computational challenges arise when applying Bayesian inference approaches to complex hierarchical models. Sampling-based inference methods, such as Markov Chain Monte Carlo strategies, are renowned for providing accurate results but with high computational costs and slow or questionable convergence. On the contrary, approximate methods like the Integrated Nested Laplace Approximation (INLA) construct a deterministic approximation to the univariate posteriors through nested Laplace Approximations. This method enables fast inference performance in Latent Gaussian Models, which encode a large class of hierarchical models. R-INLA software mainly consists of three strategies to compute all the required posterior approximations depending on the accuracy requirements. The Simplified Laplace approximation (SLA) is the most attractive because of its speed performance since it is based on a Taylor expansion up to order three of a full Laplace Approximation. Here we enhance the methodology by simplifying the computations necessary for the skewness and modal configuration. Then we propose an expansion up to order four and use the Extended Skew Normal distribution as a new parametric fit. The resulting approximations to the marginal posterior densities are more accurate than those calculated with the SLA, with essentially no additional cost.