Mathematical Sciences: Image Analysis, Spatial Statistics, and Bayesian Inference

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Markov chain Monte Carlo methods will be applied to problems in statistical inference with particular emphasis on spatial statistics and Bayesian computation. This project is highly interdisciplinary with target areas that include image analysis, whether from medical imaging, remote sensing or surface reconstruction and mapping, the analysis of data from agricultural experiments and from geographical epidemiology. There are general mathematical and computational implications for difficult issues such as multi-modality and robustness in Bayesian posterior distributions. Markov chain Monte Carlo methods have a long history in statistical physics and subsequently in spatial statistics. Now these are being applied with spectacular success to a vast range of mainstream statistical problems that have remained numerically intractable otherwise. This project, which is highly interdisciplinary because of the nature of spatial data and mapping problems, focuses on the solutions to some of the hardest problems in the analysis of data which carry spatial connotations.