Spatial Bayesian Hierarchical Modelling with Integrated Nested Laplace Approximation

TL;DR

This paper discusses the use of spatial Bayesian hierarchical models with latent Gaussian fields, employing Integrated Nested Laplace Approximation for efficient inference in applications like seismic activity and disease mapping.

Contribution

It introduces the application of INLA to spatial Bayesian models for both point pattern and areal data, demonstrating its effectiveness in real-world scenarios.

Findings

Accurate approximation of posterior distributions in spatial models

Efficient inference for complex Bayesian hierarchical models

Successful application to seismic and disease data

Abstract

We consider latent Gaussian fields for modelling spatial dependence in the context of both spatial point patterns and areal data, providing two different applications. The inhomogeneous Log-Gaussian Cox Process model is specified to describe a seismic sequence occurred in Greece, resorting to the Stochastic Partial Differential Equations. The Besag-York-Mollie model is fitted for disease mapping of the Covid-19 infection in the North of Italy. These models both belong to the class of Bayesian hierarchical models with latent Gaussian fields whose posterior is not available in closed form. Therefore, the inference is performed with the Integrated Nested Laplace Approximation, which provides accurate and relatively fast analytical approximations to the posterior quantities of interest.