Aspects of Pattern Theory.

The research in this project is motivated by pattern analysis, the study of regular structures in natural and man-made phenomena. Problems of inferring structural representations of observed patterns raise new problems of nonparametric statistical inference. The method of sieves has been developed as a general approach for adapting classical techniques of inference, such as maximum likelihood for estimation, to nonparametric settings. To develop the basic probabilistic models that form the foundation for statistical inference of patterns, characterization results have been obtained that prescribe the kinds of probability models generated by the regularity constraints of pattern theory. The mathematical questions have been studied both by analytical and computational methods. The computer experiments have led to the development of a substantial library of APL programs for mathematical experimentation. Numerous applications are described in the publications from the project. Author