Statistical Computation and Information Retrieval from Multivariate Data

在谷歌上搜索“马尔可夫链蒙特卡罗（MCMC）”，会有超过200万的点击率。这并不奇怪，因为这类算法在过去的30年里已经成为统计计算的主要工具，特别是贝叶斯推理。然而，科学实验的发展，特别是大数据的可用性和假设模型的复杂性，使MCMC到了一个拐点。当数据量很大或统计模型复杂到难以分析时，就会遇到重大困难。在前一种情况下，经典的MCMC采样器的规模差，而在后者只有近似版本的模型可以研究很少，或没有理论保证的准确性。这项研究提案的一部分涉及缩小更大的理论差距，并开发可以克服这种挑战的计算算法。 预计计算方面的重大进展将对一些处理大量数据和复杂模型的科学领域产生显著影响。赠款保持器在过去20年中一直从事计算统计工作，并为这一统计领域带来了相当多的专业知识。该提案的另一个重点涉及使用统计模型从多变量数据中提取信息。其中一个项目将通过概率方法寻求自动和数据驱动的无监督聚类策略，以确定变异的主要成分。由此产生的方法有许多潜在的应用，但将特别注意围绕申请人在这一领域获得的研究经验建立的遗传学研究。第二个项目涉及从不完全数据中估计联合分布。基于连接的结构将是建模工具，而目标应用领域包括纵向研究和抽样调查。预计由此产生的方法将为从业人员提供现有方法的强大替代方案。将通过开发免费提供的配套软件包来加强传播和应用。

A Google search with the terms "Markov chain Monte Carlo (MCMC)" returns over 2 million hits. This is not surprising, as this class of algorithms has become in the last 30 years the main workhorse for statistical computation, especially for Bayesian inference. However, the evolution of scientific experiments, particularly the availability of large data and the complexity of posited models have brought MCMC to an inflection point. Significant difficulties are encountered when the data is massive or when the statistical model is complex enough to be analytically intractable. In the former case, the classical MCMC samplers scale poorly while in the latter only approximate versions of the model can be studied with little, or no theoretical guarantees of accuracy. Part of this research proposal is concerned with closing the larger theoretical gaps and developing computational algorithms that can overcome this type of challenges. It is expected that significant progress in computation will have a marked impact on a number of scientific fields struggling with large volumes of data and complex models. The grant holder has worked in computational statistics for the last 20 years and brings considerable expertise to this area of statistics. Another focus of the proposal concerns the use of statistical models for extracting information from multivariate data. One project will pursue automatic and data-driven strategies for unsupervised clustering via probabilistic methods for determining principal components of variation. The resulting methodology has many potential applications, but special attention will be given to genetics studies built around the applicant's acquired research experience in this area. A second project involves estimation of a joint distribution from incomplete data. Copulas-based structures will be the modelling vehicle while the targeted areas of applications include longitudinal studies and sample surveys. The resulting methodology is expected to provide practitioners with robust alternatives to existing methods. Dissemination and application will be enhanced by the development of freely available companion software packages.