Statistical Computation and Information Retrieval from Multivariate Data

在谷歌上搜索“马尔科夫链蒙特卡罗(MCMC)”，搜索结果超过200万条。这并不令人惊讶，因为在过去的30年里，这类算法已经成为统计计算的主要主力，特别是贝叶斯推理。然而，科学实验的发展，特别是大量数据的可获得性和假设模型的复杂性，将MCMC带入了一个拐点。当数据庞大或统计模型复杂到难以分析时，就会遇到很大的困难。在前一种情况下，经典的MCMC采样器的规模很小，而在后一种情况下，只能研究模型的近似版本，几乎没有或没有理论上的精度保证。这项研究提案的一部分涉及填补更大的理论差距，并开发能够克服这类挑战的计算算法。预计计算方面的重大进展将对一些科学领域产生显著影响，这些领域正在为大量数据和复杂模型而苦苦挣扎。赠款持有人在过去的20年里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。一个项目将通过确定变化的主成分的概率方法，推行自动和数据驱动的无监督聚类战略。由此产生的方法有许多潜在的应用，但将特别关注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整数据中估计联合分布。基于Copulas的结构将是建模工具，而应用的目标领域包括纵向研究和抽样调查。由此产生的方法预计将为从业者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.