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**利用随机性来估计原本无法计算的数量，并**广泛应用于医学、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**工作正确，以及如何“适应”它们（即，在它们**已经运行时修改和优化它们）。这些基础问题涉及大量的数学分析和演绎，并将允许从业者更有效、更成功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到他们的应用问题上——包括**我正在进行的与心理学家分析少年犯刑事犯罪**数据的研究项目；与一位法学教授一起分析加拿大**最高法院在判决书写作中使用法律助理的情况；基于fMRI脑扫描数据分析脑不同区域血流的相关性；项目专业对学生成绩和**后续表现的影响分析当受试者发出不同的声音时，语言病理学家会分析舌头的位置。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有意义的结论

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.**