Statistical computation: theoretical results and interdisciplinary applications

我计划从理论和跨学科的角度研究统计计算问题。 在理论方面，我将继续研究广泛使用的马尔可夫链蒙特卡罗（MCMC）算法的收敛性和最优性。 这些算法 ** 使用随机性来估计否则不可能计算的数量，并且 ** 广泛用于医学，社会和计算科学的许多不同应用。我将研究诸如如何评估它们、如何改进它们、如何证明它们 ** 正在正确工作以及如何“适应”它们（即，修改和优化它们，而它们 ** 已经运行）。 这些基础问题涉及大量的数学分析和 ** 推导，并将允许从业者更有效地使用这些算法 ** 来克服许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，** 将我的统计计算专业知识应用于他们的应用问题-包括 ** 我正在进行的研究项目，心理学家分析青少年罪犯刑事犯罪 ** 数据;与一位法学教授分析加拿大 ** 最高法院在判决书撰写中使用法律助理;基于功能磁共振成像脑部扫描数据 ** 分析大脑不同区域血流的相关性;分析专业对学生成绩和 ** 后续表现的影响;并与言语病理学家一起分析受试者 ** 形成不同声音时的舌头位置。 这些应用是多种多样的，但都使用仔细的统计计算和分析来得出重要的结论。

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.**