Estimation and Inference via Computational Statistics Algorithms

为了使用复杂的统计模型*准确地分析大数据集，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，以便分析*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。*我计划使用我的NSERC研究拨款从不同的角度研究计算*统计算法，特别是马尔科夫链蒙特卡罗(MCMC)*算法。我的大部分工作将关注*算法的理论基础，*使用数学概率理论分析它们的收敛**以及性能和改进。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来自各种*主题的数据集。在所有情况下，我都将重点放在属性、性能*和这些算法的应用。*我计划*研究的一些具体的方法和理论问题包括：*如何改进流行的模式合并模拟和并行回火MCMC*算法，使高窄模式在高温下不被忽略？*当Metropolis*算法应用于比以前论文中研究的特殊情况更具*一般性的目标分布时，*算法的最佳缩放和接受率是多少？***当MCMC算法*受到轻微扰动时，其估计精度会受到什么影响？由于某些现代MCMC应用程序需要*近似计算？*“模型选择”MCMC*算法的计算复杂度如何随着参数的数量和数据量的增加而增长*如何更好地“适应”MCMC算法，以提高其*性能，同时仍收敛到正确的量？*我还计划将计算统计算法应用于各种*大型真实数据集。包括：*癌症治疗患者数据：可以发现哪些隐藏的模式*关于哪种治疗对哪类患者最有效？*学生成绩数据：什么因素影响学生选择科目*专业和未来的成功？*森林生长数据：加拿大森林中的树木种群样本的“地面真实”测量能否与来自卫星的公开图像*进行比较，以校准卫星图像以进行未来的树木估计？**

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?**