Estimation and Inference via Computational Statistics Algorithms

为了使用复杂的统计模型准确分析大型数据集，统计计算是必不可少的。所使用的算法必须高效、准确和可靠，以使分析有效和有用，并导致高质量的统计推断和关键未知量的估计。我计划用我的NSERC研究经费从各种角度研究计算统计算法，特别是马尔可夫链蒙特卡罗（MCMC）算法。我的大部分工作将关注的理论基础的算法，分析其收敛性和性能和改进使用数学概率论。我还计划研究不同的算法设计和改进。此外，我将尝试将这些算法应用于各种主题的数据集。在所有的情况下，我将集中在这些算法的属性，性能和应用。一些具体的方法和理论问题，我计划调查包括：* 如何可以流行的模式合并模拟和并行回火MCMC算法进行改进，使高窄模式不被忽略在高温下？* 什么是最佳的缩放和接受率的大都会算法时，适用于目标分布，这是更一般的特殊情况下，在以前的论文研究？* 如何是一个MCMC算法的估计精度的影响时，它是轻微的“扰动”，由于某些现代MCMC应用程序所需的近似计算？* 当参数的数量和数据的数量达到无穷大时，“模型选择”MCMC算法的计算复杂度是如何增长的？* MCMC算法如何更好地“适应”，以提高其性能，同时仍然收敛到正确的数量？我还计划将计算统计算法应用于各种大规模的真实的数据集，包括：* 癌症治疗患者数据：关于哪种药物治疗对哪种患者最有效，可以发现哪些隐藏模式？* 学生成绩数据：哪些因素影响学生的学科专业选择和未来的成功？* 森林生长数据：能否将加拿大森林树木种群样本的“地面实况”测量结果与公开的卫星图像进行比较，以校准卫星图像，用于未来的树木估计？

Statistical computation is essential in order to analyse large data sets accurately using complicated statistical models. The algorithms used have to be efficient and accurate and reliable in order for the analysis to be valid and useful, and lead to high-quality statistical inference and estimates of key unknown quantities. I plan to use my NSERC research grant to investigate computational statistics algorithms, especially Markov chain Monte Carlo (MCMC) algorithms, from a variety of perspectives. Much of my work will concern the theoretical foundations of the algorithms, analysing their convergence and performance and improvements using mathematical probability theory. I also plan to study different algorithm designs and improvements. In addition, I will try to apply these algorithms to data sets from a variety of subjects. In all cases, I will focus on the properties, performance, and application of these algorithms. Some specific methodological and theoretical questions which I plan to investigate include: * How can the popular mode-merging simulated and parallel tempering MCMC algorithms be improved so that tall narrow modes are not ignored at high temperatures? * What is the optimal scaling and acceptance rate of Metropolis algorithms when applied to target distributions which are much more general than the special cases studied in previous papers? * How is the estimation accuracy of a MCMC algorithm affected when it is slightly "perturbed", due to the approximate computations required of certain modern MCMC applications? * How does the computational complexity of "model-selection" MCMC algorithms grow as the number of parameters and amount of data go to infinity? * How can MCMC algorithms be better "adapted", to improve their performance on the fly, while still converging to the correct quantities? I also plan to apply computational statistics algorithm to various large-scale real data sets, including: * Cancer treatment patient data: What hidden patterns can be found concerning which medical treatments work best for which sorts of patients? * Student grade data: What factors influence students' choice of subject major and future success? * Forest growth data: Can "ground truth" measurements for samples of tree populations from Canadian forests be compared to publicly-available images from satellites, to calibrate the satellite images for future tree estimates?