Auxiliary Variable Markov Chain Monte Carlo for Spatial Survival and Geostatistical Models

TL;DR

This paper introduces an auxiliary variable MCMC method for spatial survival and geostatistical models that significantly reduces computational costs from O(n^3) to O(n) by using a regular grid approach, enabling efficient spatial prediction.

Contribution

The paper presents a novel auxiliary variable MCMC approach that reduces computational complexity and facilitates spatial prediction in large spatial survival and geostatistical datasets.

Findings

Computational cost reduced from O(n^3) to O(n)

Method effectively handles large spatial datasets

Enables simultaneous spatial prediction of latent functions

Abstract

This article was motivated by the desire to improve Markov chain Monte Carlo methods for spatial survival models in which the locations of individuals in space are known. For a dataset comprising information on n individuals, standard methods of MCMC-based inference involve computing the inverse of an n by n matrix at each iteration. However with a judicious choice of auxiliary variables on a regular grid with m prediction points it will be shown how to fit an essentially equivalent model but with a substantially reduced computational cost. For a fixed output grid, the computational cost of the new method is reduced from O(n^3) to O(n); the cost of increasing the output grid size being O(m\log m). Furthermore, the new method simultaneously solves the problem of spatial prediction of functions of the latent field, which for standard methods usually presents a further computational challenge. We apply the new method to a spatial survival dataset previously analysed in Henderson et. al 2002 and show how the new method can be applied to spatial and spatiotemporal geostatistical datasets with the same computational benefits.