Mathematical Sciences: Statistical Model Building with Generalized Splines

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This project develops further new mathematical, statistical and computational methods for the empirical estimation of response functions of several to many variables. Data may be direct, indirect or only on functions implicitly defined. The new spline smoothing will be extended to analysis of variance techniques. Particular problems include model selection (choice of model components to include), improved computational methods to allow efficient fitting with many variables and very large data sets, development of methods appropriate to binomial and other non-Gaussian responses and to implicit problems. Statistical models are intended to predict outcomes given specified values of the predictor variables or to describe the relationships between predictors and outcomes, or to see how responses may change as predicting factors or attributes change. Developing empirical statistical models using smoothing splines promises to be widely applicable in scientific research, ranging from the search for risk factors in large scale demographic data or for risk factors in environmental degradation, to aspects of a numerical weather forecasting system, to machine learning.