Advanced Monte Carlo Methods for Complex Statistical Models

适用于复杂统计模型的高级蒙特卡罗方法

• 批准号: 435713-2013
• 负责人: Wang, Liangliang
• 金额: $ 1.17万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=668098
• 关键词: Advanced; Monte; Carlo; Methods; Complex

Bayesian statistics has formed a unified framework for many statistical models, focusing on computing posterior distributions. The posterior computation is typically carried out by running Markov chain Monte Carlo (MCMC) algorithms. However, it is challenging to design efficient MCMC proposals for sophisticated models that require computing high-dimensional posteriors with multiple modes. Sequential Monte Carlo (SMC) methods are an alternative class of sampling algorithms that have become very popular in recent years. The objective of my research program is to develop novel SMC methodologies and combine them with MCMC for inferences of realistically complex statistical models that are traditionally approached by poorly performed MCMC methods. I will explore original applications with these methods, specifically focusing on two application areas: phylogenetics and evaluation of diagnostic tests. In phylogenetics, I propose a general evolutionary model that can incorporate various types of mutation events to study how species evolve through time and how closely species are related to each other. I also propose a novel SMC method that can efficiently sample phylogenetic trees and the mutation events. My proposed research can improve the efficiency of large-scale genetic data analysis. In the other application area - evaluation of diagnostic tests, I propose a general multivariate probit latent class model with mixed effects and a combination of SMC and MCMC for implementation in order to improve disease diagnosis and to evaluate new diagnostic tests when no gold standard diagnostic tests are available. In summary, my research program can develop efficient computing methods for inferences of sophisticated statistical modeling, which replace many heuristic or conventional methods and solve significant problems in phylogenetics and in evaluating medical diagnostic tests. My proposed methodologies can also be applied to other scientific fields such as computational biology.******

贝叶斯统计已经为许多统计模型形成了统一的框架，专注于计算后验分布。后验计算通常通过运行马尔科夫链蒙特卡罗(MCMC)算法来执行。然而，对于需要计算多个模式的高维后验信息的复杂模型，设计有效的MCMC方案是具有挑战性的。序贯蒙特卡罗(SMC)方法是近年来非常流行的一类替代抽样算法。我的研究计划的目标是开发新的SMC方法，并将它们与MCMC结合起来，以推断传统上由表现不佳的MCMC方法接近的现实复杂的统计模型。我将探索这些方法的原始应用，特别是两个应用领域：系统发生学和诊断测试的评估。在系统发育学中，我提出了一个通用的进化模型，该模型可以结合各种类型的突变事件来研究物种如何随着时间的推移而进化，以及物种之间的联系有多密切。本文还提出了一种新的SMC方法，该方法可以有效地对系统发育树和突变事件进行采样。本文提出的研究可以提高大规模遗传数据分析的效率。在另一个应用领域-诊断试验的评价中，我提出了一个具有混合效应的通用多变量Probit潜伏类模型，并将SMC和MCMC结合起来实施，以提高疾病诊断水平，并在没有金标准诊断试验的情况下对新的诊断试验进行评价。总而言之，我的研究项目可以为复杂的统计建模推理开发高效的计算方法，取代许多启发式或传统方法，并解决系统发育学和医学诊断测试评估中的重大问题。我提出的方法论也可以应用于其他科学领域，如计算生物学。