Problems in Statistical Model Building

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PROJECT ABSTRACTProblems in Statistical Model Building. Grace Wahba, PI.This research is to further the development of Smoothing Spline ANOVA and related variational methods for multivariate function estimation and statistical model building, so that these methods may be used in analyses of very large complex heterogenous data sets as occur in demographic medical studies, environmental and climatic data analyses and classification problems in a variety of areas. These methods are flexible nonparametric methods, but generally contain commonly used parametric families as special cases. The general approach proceeds in the following steps: (i)propose families of models that are appropriate for specific areas of application, (ii) develop new numerical algorithms as required for fitting the models, (ii) develop further methods for tuning the models and providing accuracy estimates, (iii) develop information concerning the properties of the methods, including testing on realistic simulated observations where the `truth' is known, (iv) and applying the resulting methods to important data sets, with the expectation of extracting information from these data that is not obtainable by standard parametric methods.The goal of this project is provide to scientists in medical, environmental and atmospheric sciences and supervised machine learning, new and useful tools to more efficiently analyze their data. Tasks are proposed to develop new methods that are appropriate for more efficient data analysis in complex demographic studies which follow populations over time, collecting information useful for understanding relationships between possible risk factors and the incidence and progression of various diseases. Tasks are also proposed for the development of new methods that are appropriate for understanding relationships among various factors of interest in large environmental and atmospheric data sets with `non-standard' indirect observational data; and for exploiting some new methods in classification that have wide applicability for building classification algorithms based on learning from large data sets in very high dimensional spaces.