Cluster Modeling and Detection

Abstract

The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying graph is unknown and needs to be inferred from the data. The second research domain dominates the applications in spatial epidemiology. In this context GGMs are typically referred to as Gaussian Markov random fields (GMRFs). Here the underlying graph is assumed to be known: the vertices correspond to geographical areas, while the edges are associated with areas that are considered to be neighbors of each other (e.g., if they share a border). We introduce multi-way Gaussian graphical models that unify the statistical approaches to inference for spatiotemporal epidemiology with the literature on general GGMs. The novelty of the proposed work consists of the addition of the G-Wishart distribution to the substantial collection of statistical tools used to model multivariate areal data. As opposed to fixed graphs that describe geography, there is an inherent uncertainty related to graph determination across the other dimensions of the data. Our new class of methods for spatial epidemiology allow the simultaneous use of GGMs to represent known spatial dependencies and to determine unknown dependencies in the other dimensions of the data. KEYWORDS: Gaussian graphical models, Gaussian Markov random fields, spatiotemporal multivariate models