Spatial Graphical Model for High-Dimensional Discrete Lattices

• Activity Number: 299
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xuan Che*+ and Alix I. Gitelman
• Companies: Oregon State University and Department of Statistics, Oregon State University
• Keywords: graphical model ; spatial statistics ; Bayesian inference ; Markov chain Monte Carlo

Abstract

The amount and dimensionality of spatial datasets have increased dramatically thanks to advancements of data collection tools. We consider the case of multivariate observations collected on a lattice, of which remotely sensed data provides a key example. For the situation where some of the components of the multivariate observation are discrete, we develop methods for specifying the multivariate joint distribution as a chain graph with both discrete and continuous components, and with spatial dependencies assumed among all variables on the lattice. We propose a new group of chain graphs, generalized tree networks, and, by constructing the chain graph as a generalized tree network, partition its joint distribution according to the maximal cliques of the graph. We then use a Gaussian Copula transformation to model spatial dependence among the discrete variables in the cliques. We demonstrate our method using simulated data and also apply it to a remote sensing dataset.