Statistical Computation and Information Retrieval from Multivariate Data

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A Google search with the terms "Markov chain Monte Carlo (MCMC)" returns over 2 million hits. This is not surprising, as this class of algorithms has become in the last 30 years the main workhorse for statistical computation, especially for Bayesian inference. However, the evolution of scientific experiments, particularly the availability of large data and the complexity of posited models have brought MCMC to an inflection point. Significant difficulties are encountered when the data is massive or when the statistical model is complex enough to be analytically intractable. In the former case, the classical MCMC samplers scale poorly while in the latter only approximate versions of the model can be studied with little, or no theoretical guarantees of accuracy. Part of this research proposal is concerned with closing the larger theoretical gaps and developing computational algorithms that can overcome this type of challenges. It is expected that significant progress in computation will have a marked impact on a number of scientific fields struggling with large volumes of data and complex models. The grant holder has worked in computational statistics for the last 20 years and brings considerable expertise to this area of statistics. Another focus of the proposal concerns the use of statistical models for extracting information from multivariate data. One project will pursue automatic and data-driven strategies for unsupervised clustering via probabilistic methods for determining principal components of variation. The resulting methodology has many potential applications, but special attention will be given to genetics studies built around the applicant's acquired research experience in this area. A second project involves estimation of a joint distribution from incomplete data. Copulas-based structures will be the modelling vehicle while the targeted areas of applications include longitudinal studies and sample surveys. The resulting methodology is expected to provide practitioners with robust alternatives to existing methods. Dissemination and application will be enhanced by the development of freely available companion software packages.