Scaling priors in two dimensions for Intrinsic Gaussian MarkovRandom Fields

TL;DR

This paper investigates how to effectively scale two-dimensional Intrinsic Gaussian Markov Random Fields (IGMRFs) by linking the scaling parameter to the marginal standard deviation, impacting Bayesian model inference.

Contribution

It introduces a method for tuning the scaling parameter in 2D IGMRFs via marginal standard deviation, enhancing model accuracy and interpretability.

Findings

Scaling significantly affects posterior results.

Mapping to marginal standard deviation improves tuning.

Application to blood pressure data demonstrates practical benefits.

Abstract

Intrinsic Gaussian Markov Random Fields (IGMRFs) can be used to induce conditional dependence in Bayesian hierarchical models. IGMRFs have both a precision matrix, which defines the neighbourhood structure of the model, and a precision, or scaling, parameter. Previous studies have shown the importance of selecting this scaling parameter appropriately for different types of IGMRF, as it can have a substantial impact on posterior results. Here, we focus on the two-dimensional case, where tuning of the parameter is achieved by mapping it to the marginal standard deviation of a two-dimensional IGMRF. We compare the effects of scaling various classes of IGMRF, including an application to blood pressure data using MCMC methods.