Non-Stationary Models for Spatial Statistics and Bayesian Image Analysis

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NSF DMS-9704425 Non-Stationary Models for Spatial Statistics and Bayesian Image Analysis. David Higdon Duke University Abstract: This research develops anisotropic spatial models for fully Bayesian inference with applications to data which are correlated over space and time. Two distinct directions are taken. First, in continuation of previous research, Markov random field priors for lattices are considered for modeling processes with occasional large shifts in level. Second, using a constructive convolution approach, continuous models are developed that allow non-stationarity and correlation structure that can vary over space (and/or time). Using such models for inference requires that one account for uncertainty about just how flexible or varying such models are. A key part of the research is developing methods which incorporate this source of uncertainty in the statistical analysis. Statistical modeling of phenomena that evolve over space and possibly time is critical in areas such as medical imaging, environmental monitoring, and detecting changes over time in global climate. Most spatial models in statistics assume that over a given area, the underlying properties of a spatial (and possibly temporal as well) pattern remain unchanged over the region. Though this is a useful simplification over limited regions, on a larger scale such an assumption often results in an unsatisfactory model. This research will develop statistical models that account for abrupt changes in the nature of the spatial phenomenon. Also, models will be developed that allow properties of the spatial process to evolve over spatial location. This research will lead to more realistic models for large scale spatial and spatio-temporal phenomena. Fitting these models to large datasets will require a substantial computing effort and will likely rely high performance computing resources. Applications in global ocean climate change, agriculture, genetics, and medical imaging will be considered.