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December 2020 Intuitive Joint Priors for Variance Parameters
Geir-Arne Fuglstad, Ingeborg Gullikstad Hem, Alexander Knight, Håvard Rue, Andrea Riebler
Bayesian Anal. 15(4): 1109-1137 (December 2020). DOI: 10.1214/19-BA1185

Abstract

Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a tree structure to the individual model components. For each split in the tree, an analyst may be ignorant or have a sound intuition on how to attribute variance to the branches. In the former case a Dirichlet prior is appropriate to use, while in the latter case a penalised complexity (PC) prior provides robust shrinkage. A bottom-up combination of the conditional priors results in a proper joint prior. We suggest default values for the hyperparameters and offer intuitive statements for eliciting the hyperparameters based on expert knowledge. The prior framework is applicable for R packages for Bayesian inference such as INLA and RStan.

Three simulation studies show that, in terms of the application-specific measures of interest, PC priors improve inference over Dirichlet priors when used to penalise different levels of complexity in splits. However, when expressing ignorance in a split, Dirichlet priors perform equally well and are preferred for their simplicity. We find that assigning current state-of-the-art default priors for each variance parameter individually is less transparent and does not perform better than using the proposed joint priors. We demonstrate practical use of the new framework by analysing spatial heterogeneity in neonatal mortality in Kenya in 2010–2014 based on complex survey data.

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Geir-Arne Fuglstad. Ingeborg Gullikstad Hem. Alexander Knight. Håvard Rue. Andrea Riebler. "Intuitive Joint Priors for Variance Parameters." Bayesian Anal. 15 (4) 1109 - 1137, December 2020. https://doi.org/10.1214/19-BA1185

Information

Published: December 2020
First available in Project Euclid: 30 October 2019

Digital Object Identifier: 10.1214/19-BA1185

Keywords: Additive models , hierarchical variance decomposition , joint prior distributions , latent Gaussian models , penalised complexity , variance parameters

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Vol.15 • No. 4 • December 2020
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