Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family. Issue 532 (11th December 2020)

• Record Type: Journal Article
• Authors: Bradley, Jonathan R.; Holan, Scott H.; Wikle, Christopher K.
• Is Part Of: Journal of the American Statistical Association. Volume 115:Issue 532(2020)
• Page Start: 2037
• Page End: 2052
• Publication Date: 2020-12-11
• Subjects: Bayesian hierarchical model -- Big data -- Exponential family -- Gibbs sampler -- Markov chain Monte Carlo -- Non-Gaussian; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2019.1677471
• Languages: English
• ISSNs: 0162-1459

Abstract

Abstract: 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 the "conjugate multivariate distribution, " which is motivated by the Diaconis and Ylvisaker distribution. 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. To demonstrate the wide-applicability of the proposed methodology, we provide two simulation studies and three applications based on an epidemiology dataset, a federal statistics dataset, and an environmental dataset, respectively. Supplementary materials for this article are available online.