10.6084/m9.figshare.11307437.v1 Jonathan R. Bradley Jonathan R. Bradley Scott H. Holan Scott H. Holan Christopher K. Wikle Christopher K. Wikle Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family Taylor & Francis Group 2019 Bayesian hierarchical model Big data Exponential family Gibbs sampler Markov chain Monte Carlo Non-Gaussian 2019-12-03 00:42:12 Dataset https://tandf.figshare.com/articles/dataset/Bayesian_Hierarchical_Models_With_Conjugate_Full-Conditional_Distributions_for_Dependent_Data_From_the_Natural_Exponential_Family/11307437 <p>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 <i>n</i> problem.” The computational complexity of the “big <i>n</i> 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. <a href="https://doi.org/10.1080/01621459.2019.1677471" target="_blank">Supplementary materials</a> for this article are available online.</p>