Statistical computation: theoretical results and interdisciplinary applications

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I plan to study statistical computation issues from both theoretical and interdisciplinary perspectives. On the theoretical side, I will continue to investigate convergence and optimality properties of the widely-used Markov chain Monte Carlo (MCMC) algorithms. These algorithms use randomness to estimate quantities which would otherwise be impossible to compute, and are widely used in the medical, social, and computational sciences for many different applications. I will study such issues as how to evaluate them, how to improve them, how to prove that they are working correctly, and how to "adapt" them (i.e., modify and optimise them while they are already running). Such foundational questions involve lots of mathematical analysis and deduction, and will allow practitioners to use these algorithms more efficiently and successfully to overcome computational challenges which arise in numerous scientific enterprises. On the applications side, I plan to collaborate with researchers in a variety of disciplines, to bring my statistical computation expertise to bear on their applied problems -- including my ongoing research projects with psychologists analysing juvenile offender criminal offense data; with a law professor analysing the use of law clerks in judgment writing on the Canadian Supreme Court; analysing correlations of blood flow in different regions of the brain based on fMRI brain-scan data; analysing of the influence of program major on student grades and subsequent performance; and with a speech pathologist analysing tongue positions when subjects form different sounds. These applications are many and varied, but all use careful statistical computation and analysis to derive significant conclusions.