Mathematical Sciences: Robustness and Scale in Spatial Applications of Markov Chain Monte Carlo for Bayesian Inference

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Proposal: DMS9505114 PI: Dave Higdon Institution: Duke University Title: Robustness and Scale in Spatial Applications of Markov Chain Monte Carlo for Bayesian Inference Abstract: The proposed research develops flexible prior distributions for Bayesian inference for spatial systems. From the modeling standpoint, spatial priors that are mixtures over simple Markov random fields (MRF's) are developed in two distinct contexts. In the first, mixtures will be constructed to allow robust inference when anomalies, and heterogeneity are present in the spatial process. In the second context, mixtures over different scales will be considered, so that the scale of the MRF can be rigorously treated as a parameter when making inference. Only very recent advances in Markov chain Monte Carlo (MCMC) make inference from such models possible. Applications in agriculture, imaging and environmental monitoring will be considered. The proposed research will develop statistical methodologies for analyzing spatial data which combines information at various scales. Development of spatial models suitable for agriculture, imaging (eg. remote sensing and medical imaging), environmental monitoring and assessing environmental trends are main goals of this research. Current statistical methods typically require restrictive assumptions which often make formal analyses in these areas difficult or impossible. This methodology will relax these assumptions. A primary motivation for combining information from various scales is for dealing with geographical information systems used for environmental monitoring. Such systems invariably contain data at varying scales which can be incorporated in the analysis.