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Activity Number: 492 - Recent Advances in Modeling Complex Dependent Data
Type: Invited
Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
Sponsor: Business and Economic Statistics Section
Abstract #326917 Presentation
Title: Hierarchical Models with Conditionally Conjugate Full-Conditional Distributions for Dependent Data from the Natural Exponential Family
Author(s): Jonathan R Bradley* and Scott H. Holan and Christopher K. Wikle
Companies: Florida State University and University of Missouri/U.S. Census Bureau and University of Missouri
Keywords: Bayesian Analysis; Conjugate; Big Data

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural 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 the "big n problem" is further exacerbated when allowing for non-Gaussian data models, as is the case here. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce something we call the "conjugate multivariate distribution," which is motivated by the univariate distribution introduced in Diaconis and Ylvisaker (1979). Furthermore, we provide substantial theoretical and methodological development including: results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, conjugate prior distributions, and full-conditional distributions for a Gibbs sampler. We demonstrate the proposed methodology through simulated examples and real-data analyses, including application to the Longitudinal Employer-Household Dynami

Authors who are presenting talks have a * after their name.

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