Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family

By Jonathan R. Bradley, Scott H. Holan, Christopher K. Wikle. 2017

62 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dde9deae3bfc87343f8141ba0234240883b819b4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. A. Zammit‐Mangion
2. Matthew Sainsbury-Dale
3. Noel Cressie

In Statistics and Probability

1. A. Zammit‐Mangion
2. Matthew Sainsbury-Dale
3. Noel Cressie
4. Finn Lindgren
5. Francky Fouedjio

Citations in the corpus

• Basis-Function Models in Spatial Statistics (2021, methodology): “Various generalisations of Equation 37 are possible; for instance, one may relate Zt and Y t via a linear or non-linear mapping, such as discussed in Cressie & Wikle (2011, Sec. 7.1). Basis functions have often been used in dynamic spatio-temporal models, such as in Wikle & Cressie (1999), Wikle et ”