Design and Structure Dependent Priors for Scale Parameters in Latent Gaussian Models

TL;DR

This paper introduces a novel approach for specifying priors on scale parameters in latent Gaussian models by focusing on the marginal prior of a dispersion measure, simplifying prior elicitation and improving inference.

Contribution

It proposes a method to specify priors based on a dispersion measure, deriving the implied prior for scale parameters, and evaluates its effectiveness through simulations and real data applications.

Findings

The proposed prior elicitation method improves estimator properties.

Simulation results demonstrate favorable sampling behavior.

Real data analysis shows sensitivity and variance allocation benefits.

Abstract

Many common correlation structures assumed for data can be described through latent Gaussian models. When Bayesian inference is carried out, it is required to set the prior distribution for scale parameters that rules the model components, possibly allowing to incorporate prior information. This task is particularly delicate and many contributions in the literature are devoted to investigating such aspects. We focus on the fact that the scale parameter controls the prior variability of the model component in a complex way since its dispersion is also affected by the correlation structure and the design. To overcome this issue that might confound the prior elicitation step, we propose to let the user specify the marginal prior of a measure of dispersion of the model component, integrating out the scale parameter, the structure and the design. Then, we analytically derive the implied prior for the scale parameter. Results from a simulation study, aimed at showing the behavior of the estimators sampling properties under the proposed prior elicitation strategy, are discussed. Lastly, some real data applications are explored to investigate prior sensitivity and allocation of explained variance among model components.