Bayesian spatial cluster signal learning with application to adverse event (AE).

There is growing interest in understanding geographic patterns of medical device-related adverse events (AEs). A spatial scan method combined with the likelihood ratio test (LRT) for spatial-cluster signal detection over the geographical region is universally used. The spatial scan method used a moving window to scan the entire study region and collected some candidate sub-regions from which the spatial-cluster signal(s) will be found. However, it has some challenges, especially in computation. First, the computational cost increased when the number of sub-regions increased. Second, the computational cost may increase if a large spatial-cluster pattern is present and a flexible-shaped window is used. To reduce the computational cost, we propose a Bayesian nonparametric method that combines the ideas of Markov random field (MRF) to leverage geographical information to find potential signal clusters. Then, the LRT is applied for the detection of spatial cluster signals. The proposed method provides an ability to capture both locally spatially contiguous clusters and globally discontiguous clusters, and is manifested to be effective and tractable using hypothetical Left Ventricular Assist Device (LVAD) data as an illustration.

Time fused coefficient SIR model with application to COVID-19 epidemic in the United States.

In this paper, we propose a Susceptible-Infected-Removal (SIR) model with time fused coefficients. In particular, our proposed model discovers the underlying time homogeneity pattern for the SIR model's transmission rate and removal rate via Bayesian shrinkage priors. MCMC sampling for the proposed method is facilitated by the nimble package in R. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. We further apply the proposed methodology to analyze different levels of COVID-19 data in the United States.

Bayesian Variable Selection for Pareto Regression Models with Latent Multivariate Log Gamma Process with Applications to Earthquake Magnitudes.

Generalized linear models are routinely used in many environment statistics problems such as earthquake magnitudes prediction. Hu et al. proposed Pareto regression with spatial random effects for earthquake magnitudes. In this paper, we propose Bayesian spatial variable selection for Pareto regression based on Bradley et al. and Hu et al. to tackle variable selection issue in generalized linear regression models with spatial random effects. A Bayesian hierarchical latent multivariate log gamma model framework is applied to account for spatial random effects to capture spatial dependence. We use two Bayesian model assessment criteria for variable selection including Conditional Predictive Ordinate (CPO) and Deviance Information Criterion (DIC). Furthermore, we show that these two Bayesian criteria have analytic connections with conditional AIC under the linear mixed model setting. We examine empirical performance of the proposed method via a simulation study and further demonstrate the applicability of the proposed method in an analysis of the earthquake data obtained from the United States Geological Survey (USGS).