Fitting Stochastic Partial Differential Equations to Spatial Data
Final rept. 1 Oct 1989-30 Sep 1993
COLORADO UNIV HEALTH SCIENCES CENTER DENVER
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The research under this project was aimed at developing numerical methods for fitting stochastic partial differential equations to irregularly spaced spatial data. This is related to two dimensional smoothing spline fitting where the partial differential equation is the Laplacian driven by white noise. A class of continuous two dimensional spatial autoregressive, moving average ARMA models were investigated and numerical methods developed to implement fitting these models to spatial data. The spatial ARMA models provide a complete class of covariance structures rather than a very limited set of covariance functions that are typically used in Kriging. Since maximum likelihood methods are used to fit the models, methods such as likelihood ratio tests and Akaikes Information Criterion AIC can be used for model selection. Prediction maps can then be calculated at a grid of points, and contour maps drawn. Also maps can be drawn of the standard deviation of the predicted fields giving indications of the variability of the predictions. Applications include aquifer heights, coal field depth and thickness and snowfall amounts. Results have been presented in a number of presentations and publications.
- Numerical Mathematics