Statistical Theory and Methodology

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Abstract:This project aims to develop theoretical ideas in mathematical statistics and probability that will be of genuine use to scientific practitioners. The current proposal concerns five major projects: a detailed look at Markov Chain Monte Carlo methods, in particular the eigenvalue theory that determines rates of convergence; the application of MCMC theory to truncated data; inferential theory for scatterplot smoothers, including the relative efficiencies of competing criteria adaptively selecting the "window width" of the smoother, and also the cost of adaptation on the accuracy of the smoother; random matrix theory and its connection with the zeros of Riemann's zeta function; and finally conversion curve methods for improving the accuracy of bootstrap confidence intervals. The connecting theme for the five projects is the combination of mathematical theory with computer-intensive algorithms.