Complex Statistical Models: Theory and Methodology for Scientific Applications

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Complex Statistical Models: Theory and Methodologyfor Scientific ApplicationsLarry Wasserman, Christopher Genovese, Robert E. Kassand Kathryn RoederABSTRACTThis project is aimed at developing statistical theory and methodology for highly complex, possibly infinite dimensional models. Although the methodology and theory will be quite general, we will conduct the researchin the context of three scientific collaborations. The first is ``Characterizing Large-Scale Structure in the Universe,'' a joint project with astrophysicists and computer scientists. The main statistical challenges are nonparametric density estimation and clustering, subject to highly non-linear constraints. The second project is ``Locating Disease Genes with Genomic Control.'' We aim to locate regions of the genome with more genetic similarity among cases (subjects with disease) than controls. These regions are candidates for containing disease genes. Finding these regions ina statistically rigorous fashion requires testing a vast number of hypotheses. We will extend and develop recent techniques for multiple hypothesis testing.The third projects is ``Modeling Neuron Firing Patterns.'' The goal is to construct and fit models for neuron firing patterns, called spike trains. The data consist of simultaneous voltage recordings of numerous neurons which have been subjected to time-varying stimuli. The data are correlated over time and a major effort is to develop a class of models, called inhomogeneous Markov interval (IMI) process models, which can adequately represent the data.Statistical methods for simple statistical models with a small number of parameters are well established.These models often do not provide an adequate representation of the phenomenon under investigation.Currently, scientists are deluged with huge volumes of high quality data. These data afford scientists the opportunity to use very complex models that more faithfully reflect reality. The researchers involved in this proposal are developing methodology and theory for analyzing data from these complex models. The methods are very general but they are being developed for applications in Astrophysics, Genetics and Neuroscience.