Default Bayesian analysis for multivariate generalized CAR models

Abstract

In recent years, multivariate spatial models have been proven to be an effective tool for analyzing spatially related multidimensional data arising from a common underlying spatial process. Currently, the Bayesian analysis is perhaps the only solution available in this framework where prior selection plays an important role in the inference. The present article contributes towards the development of Bayesian inferential methodology for multivariate generalized linear mixed models, in particular, multivariate conditional autoregressive (CAR) models. The two main contributions of this article are the development of a shrinkage-type default prior for the covariance matrices and innovative computational techniques for the Gibbs sampling implementation. The default prior elicitation is non-informative but results in a proper posterior on the related parameter spaces. This elicitation not only provides robust inference (with respect to prior choice), but also provides improved estimation. In the computational step, we have developed a transformation of the parameters that avoids sampling from restricted domains, thus providing more stability and efficiency in the Gibbs implementation. The methodology has been extended to the case of missing responses in the multi-dimensional setup. Both simulations and real examples are provided to validate and illustrate the proposed methodology.

Variable Selection for Binary Spatial Regression: Penalized Quasi-Likelihood Approach

“…That is, with where is the estimated population at risk for the i ‐th county and is calculated by considering the age‐adjusted risk at both the county level and population level. The explicit formula can be found in Dass et al (). Simulation study shows that the variable selection approaches tends to select more covariates as correlation between covariates is getting stronger.…”