Estimation and Inference via Computational Statistics Algorithms

通过计算统计算法进行估计和推理

• 批准号: RGPIN-2019-04142
• 负责人: Rosenthal, Jeffrey
• 金额: $ 3.86万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=714660
• 关键词: Estimation; Inference; via; Computational; Statistics

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?

为了分析大型数据集，统计计算是必不可少的 准确地使用复杂的统计模型。 使用的算法有 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， 关键未知量的估计。 我计划用我的NSERC研究经费来研究计算 统计算法，特别是马尔可夫链蒙特卡罗（MCMC） 算法，从各种角度来看。 我的大部分工作将涉及 算法的理论基础，分析其收敛性 以及性能和改进。 我 也计划研究不同的算法设计和改进。 在 此外，我将尝试将这些算法应用于各种数据集， 的主题。 在所有情况下，我将重点放在属性，性能， 以及这些算法的应用。 一些具体的方法论和理论问题，我计划 调查包括： * 如何将流行的模式合并模拟和并行回火MCMC 算法得到改进，使高窄模式不会被忽略，在高 温度？ * 大都会的最佳规模和接受率是多少 算法时，适用于目标分布，这是更多 一般比特殊情况下研究在以前的文件？ * MCMC算法的估计精度如何受到影响 由于需要近似计算， 某些现代MCMC应用程序？ * “模型选择”MCMC的计算复杂度如何 算法随着参数数量和数据量的增加而增长， 无穷大？ * MCMC算法如何更好地“适应”，以提高其 在飞行中的性能，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 大型真实的数据集，包括： * 癌症治疗患者数据：可以发现哪些隐藏模式 哪种治疗方法对哪种病人最有效 * 学生成绩数据：哪些因素影响学生选考科目 未来的成功和成功？ * 森林生长数据：树木样本的“地面实况”测量 加拿大森林中的种群与公开提供的图像进行比较 从卫星上，校准卫星图像，为未来的树木估计？