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Spatial Disease Mapping Using Directed Acyclic Graph Auto-Regressive (DAGAR) Models

Spatial Disease Mapping Using Directed Acyclic Graph Auto-Regressive (DAGAR) Models Bayesian Analysis (2019) 14, Number 4, pp. 1221–1244 Spatial Disease Mapping Using Directed Acyclic Graph Auto-Regressive (DAGAR) Models ∗¶ † ‡ § Abhirup Datta , Sudipto Banerjee , James S. Hodges , and Leiwen Gao Abstract. Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix incorporates the spatial dependence between the regions. Common choices for the precision matrix include the widely used ICAR model, which is singular, and its nonsingular extension which lacks interpretability. We propose a new parametric model for the precision matrix based on a directed acyclic graph (DAG) repre- sentation of the spatial dependence. Our model guarantees positive definiteness and, hence, in addition to being a valid prior for regional spatially correlated ran- dom effects, can also directly model the outcome from dependent data like images and networks. Theoretical results establish a link between the parameters in our model and the variance and covariances of the random effects. Simulation stud- ies demonstrate that the improved interpretability of our model reaps benefits in terms of accurately recovering the latent spatial random effects as well as for http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bayesian Analysis Unpaywall

Spatial Disease Mapping Using Directed Acyclic Graph Auto-Regressive (DAGAR) Models

Bayesian AnalysisDec 1, 2019
24 pages

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Publisher
Unpaywall
ISSN
1931-6690
DOI
10.1214/19-ba1177
Publisher site
See Article on Publisher Site

Abstract

Bayesian Analysis (2019) 14, Number 4, pp. 1221–1244 Spatial Disease Mapping Using Directed Acyclic Graph Auto-Regressive (DAGAR) Models ∗¶ † ‡ § Abhirup Datta , Sudipto Banerjee , James S. Hodges , and Leiwen Gao Abstract. Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix incorporates the spatial dependence between the regions. Common choices for the precision matrix include the widely used ICAR model, which is singular, and its nonsingular extension which lacks interpretability. We propose a new parametric model for the precision matrix based on a directed acyclic graph (DAG) repre- sentation of the spatial dependence. Our model guarantees positive definiteness and, hence, in addition to being a valid prior for regional spatially correlated ran- dom effects, can also directly model the outcome from dependent data like images and networks. Theoretical results establish a link between the parameters in our model and the variance and covariances of the random effects. Simulation stud- ies demonstrate that the improved interpretability of our model reaps benefits in terms of accurately recovering the latent spatial random effects as well as for

Journal

Bayesian AnalysisUnpaywall

Published: Dec 1, 2019

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