HIERARCHICAL BAYESIAN CURVE FITTING AND MODEL CHOICE FOR SPATIAL DATA
A model choice criterion is developed and applied to spatial smoothing and curve fitting problems. The underlying regression function is modelled as the sum of a polynomial with random coefficients and a Gaussian random process by expanding it in a Taylor series. Two nested models, a nonadditive full model and an additive reduced model, are thus obtained for the data depending on whether the mixed partial derivatives of the regression function are retained in the model. The problem is then formulated as a general linear model and a hierarchical Bayesian approach is used to study it. This approach readily lends itself to the development of a model choice criterion by examining the Bayes factor of the full nonadditive model relative to the reduced additive model. Once the model is chosen, the hierarchical Bayesian approach is again available for curve fitting and smoothing based on this model. Simulated and real applications are provided for illustrating the methodology.