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Tracking and estimating Daily Fine Particulate Matter (PM2.5) is veryimportant as it has been shown that PM2.5 is directly related to mortalityrelated to lungs, cardiovascular system, and stroke. That is, high values ofPM2.5 constitute a public health problem in the US, and it is important that weprecisely estimate PM2.5 to aid in public policy decisions. Thus, we propose aBayesian hierarchical model for high-dimensional "multi-type" responses. By"multi-type" responses we mean a collection of correlated responses that havedifferent distributional assumptions (e.g., continuous skewed observations, andcount-valued observations). The Centers for Disease Control and Prevention(CDC) database provides counts of mortalities related to PM2.5 and dailyaveraged PM2.5 which are both treated as responses in our analysis. Our modelcapitalizes on the shared conjugate structure between the Weibull (to modelPM2.5), Poisson (to model diseases mortalities), and multivariate log-gammadistributions, and we use dimension reduction to aid with computation. Ourmodel can also be used to improve the precision of estimates and estimatevalues at undisclosed/missing counties. We provide a simulation study toillustrate the performance of the model, and give an in-depth analysis of theCDC dataset.

Latent Multivariate Log-Gamma Models for High-Dimensional Multi-Type  Responses with Application to Daily Fine Particulate Matter and Mortality  Counts