Statistical computation: theoretical results and interdisciplinary applications

我计划从理论和跨学科两方面研究统计计算问题 视角 在理论方面，我将继续研究收敛性和最优性 广泛使用的马尔可夫链蒙特卡罗（MCMC）算法的性能。 这些算法 使用随机性来估计否则不可能计算的数量， 广泛用于医学、社会和计算科学中的许多不同应用。 我将研究如何评价它们，如何改进它们，如何证明它们 正确地工作，以及如何“适应”它们（即，修改和优化它们， 已经运行）。 这些基础问题涉及大量的数学分析， 演绎，并将使从业者能够更有效、更成功地使用这些算法 以克服在众多科学企业中出现的计算挑战。 在应用方面，我计划与不同学科的研究人员合作， 把我的统计计算专业知识运用到他们的应用问题上--包括 我正在进行的研究项目与心理学家分析青少年罪犯的刑事犯罪 数据;与一位法学教授分析了在加拿大的判决书写作中使用法律助理 最高法院;分析大脑不同区域血流的相关性， 对脑功能磁共振成像扫描数据，分析专业对学生成绩的影响， 随后的表现;和语言病理学家分析舌头的位置时， 形成不同的声音。 这些应用程序是多种多样的，但都使用仔细的统计 通过计算和分析得出重要结论。

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.