Abstract:
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We introduce a Bayesian approach for analyzing high-dimensional dependent data that are distributed according to a member from the exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called "big n problem." The computational complexity of this problem is further exacerbated by allowing for non-Gaussian data models. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce a class of conjugate multivariate distributions for the exponential family. We discuss several theoretical results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, parameter models, and full-conditional distributions for a Gibbs sampler. We demonstrate the modeling framework through several examples, including an analysis of a large dataset consisting of American Community Survey (ACS) period estimates.
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