Research in Bayesian Analysis: Large-scale Regression and Prediction Models with Applications in Bioinformatics and Applied Time Series

PI，合作者和学生为涉及大型复杂数据集潜在结构的问题开发统计模型和方法。 具体研究课题包括：新的回归和预测模型与潜变量;一系列的发展，涉及潜在的结构贝叶斯回归模型和相关的算法实现使用模拟方法;统计方面的机器学习算法的回归和分类;广义线性和多变量的潜在因素模型;模型与错误的预测变量;经验因素模型。这些领域的研究部分是由于生物信息学在基因表达谱领域的应用，以及金融和通信信号处理中时间序列的相关研究和应用，这项研究涉及创建和实施改进的方法，对功能基因组学、金融和通信工程等领域产生的大型复杂数据集进行统计分析。 研究目标包括创建新的数学模型，可以充分代表日益庞大的数据集的复杂结构，以及使用这些模型分析此类数据的适当计算工具和算法。 由于基因组技术的快速发展，越来越大和复杂的基因表达数据集正在成为生物医学研究的标准，这一研究的主要方面涉及功能基因组学的应用，从而带来了分析挑战，突出了在这一统计研究领域取得重大进展的必要性。 从本研究中产生的模型的其他应用在于在金融和通信等领域产生的时间序列数据的分析。

The PI, collaborators and students develop statistical models and methods for problems involving latent structure in large and complex data sets. Specific research topics include: new models for regression and prediction with latent variables; a range of developments involving latent structure in Bayesian regression models and associated algorithmic implementation using simulation methods; statistical aspects of machine learning algorithms for regression and classification; generalized linear and multivariate latent factor models; models with errors in predictor variables; empirical factor models. Research in these areas is partly motivated by applications in bioinformatics in the area of gene expression profiling, and related research and applications in time series in finance and communications signals processing.This research is concerned with creating and implementing improved methods for the statistical analysis of large and complex data sets arising in fields such as functional genomics, finance and communications engineering. The research goals include creating new mathematical models that can adequately represent the complex structure of increasingly large data sets, together with appropriate computational tools and algorithms for the analysis of such data using these models. The need for substantial advances in this area of statistical research are highlighted by the analysis challenges posed by the increasingly large and complex gene expression data sets that are becoming standard in biomedical research due to rapid advances in genome technology, and major aspects of this research involve applications in functional genomics. Additional applications of models arising from this research lie in analysis of time series data arising in areas including finance and communications.