In this paper, we consider the problem of specifying priors for the variance components in the Bayesian analysis of the Besag-York-Molli´e model, a model that is popular among epidemiologists for disease mapping. The model encompasses two sets of random effects: one spatially structured to model spatial autocorrelation and the other spatially unstructured to describe residual heterogeneity. In this model, prior specification for variance components is an important problem because these priors maintain their influence on the posterior distributions of relative risks when mapping rare diseases. We propose using generalised inverse Gaussian priors, a broad class of distributions that includes many distributions commonly used as priors in this context, such as inverse gammas. We discuss the prior parameter choice with the aim of balancing the prior weight of the two sets of random effects on total variation and controlling the amount of shrinkage. The suggested prior specification strategy is compared to popular alternatives using a simulation exercise and applications to real data sets.

Enrico, F., Greco, F.P., Trivisano, C. (2016). On the specification of prior distributions for variance components in disease mapping models. STATISTICA, 76(1), 93-111 [10.6092/issn.1973-2201/6319].

On the specification of prior distributions for variance components in disease mapping models

GRECO, FEDELE PASQUALE;TRIVISANO, CARLO
2016

Abstract

In this paper, we consider the problem of specifying priors for the variance components in the Bayesian analysis of the Besag-York-Molli´e model, a model that is popular among epidemiologists for disease mapping. The model encompasses two sets of random effects: one spatially structured to model spatial autocorrelation and the other spatially unstructured to describe residual heterogeneity. In this model, prior specification for variance components is an important problem because these priors maintain their influence on the posterior distributions of relative risks when mapping rare diseases. We propose using generalised inverse Gaussian priors, a broad class of distributions that includes many distributions commonly used as priors in this context, such as inverse gammas. We discuss the prior parameter choice with the aim of balancing the prior weight of the two sets of random effects on total variation and controlling the amount of shrinkage. The suggested prior specification strategy is compared to popular alternatives using a simulation exercise and applications to real data sets.
2016
Enrico, F., Greco, F.P., Trivisano, C. (2016). On the specification of prior distributions for variance components in disease mapping models. STATISTICA, 76(1), 93-111 [10.6092/issn.1973-2201/6319].
Enrico, Fabrizi; Greco, FEDELE PASQUALE; Trivisano, Carlo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/568930
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