Complex Statistical Models: Theory and Methodology for Scientific Applications

复杂统计模型：科学应用的理论和方法拉里·沃瑟曼，克里斯托弗·吉诺维斯，罗伯特·e·卡森和凯瑟琳·罗德摘要本项目旨在为高度复杂的，可能是无限维的模型发展统计理论和方法。虽然方法和理论将相当普遍，但我们将在三个科学合作的背景下进行研究。第一个是天体物理学家和计算机科学家的联合项目“描绘宇宙中的大规模结构”。主要的统计挑战是非参数密度估计和聚类，受高度非线性约束。第二个项目是“用基因组控制定位疾病基因”。“我们的目标是找到病例（疾病受试者）中遗传相似性高于对照组的基因组区域。这些区域是包含疾病基因的候选区域。要在统计上严谨地找到这些区域，需要检验大量的假设。我们将扩展和发展多元假设检验的最新技术。第三个项目是“神经元放电模式建模”。“目标是构建和拟合神经元放电模式的模型，称为尖峰序列。这些数据是由同时受到时变刺激的许多神经元的电压记录组成的。随着时间的推移，数据是相关的，主要的工作是开发一类模型，称为非齐次马尔可夫区间（IMI）过程模型，它可以充分表示数据。具有少量参数的简单统计模型的统计方法已经很好地建立起来。这些模型往往不能充分反映所调查的现象。目前，科学家们被大量高质量的数据淹没了。这些数据使科学家有机会使用更真实地反映现实的非常复杂的模型。参与这项提议的研究人员正在开发分析这些复杂模型数据的方法和理论。这些方法是非常通用的，但它们正在开发应用于天体物理学、遗传学和神经科学。

Complex Statistical Models: Theory and Methodologyfor Scientific ApplicationsLarry Wasserman, Christopher Genovese, Robert E. Kassand Kathryn RoederABSTRACTThis project is aimed at developing statistical theory and methodology for highly complex, possibly infinite dimensional models. Although the methodology and theory will be quite general, we will conduct the researchin the context of three scientific collaborations. The first is ``Characterizing Large-Scale Structure in the Universe,'' a joint project with astrophysicists and computer scientists. The main statistical challenges are nonparametric density estimation and clustering, subject to highly non-linear constraints. The second project is ``Locating Disease Genes with Genomic Control.'' We aim to locate regions of the genome with more genetic similarity among cases (subjects with disease) than controls. These regions are candidates for containing disease genes. Finding these regions ina statistically rigorous fashion requires testing a vast number of hypotheses. We will extend and develop recent techniques for multiple hypothesis testing.The third projects is ``Modeling Neuron Firing Patterns.'' The goal is to construct and fit models for neuron firing patterns, called spike trains. The data consist of simultaneous voltage recordings of numerous neurons which have been subjected to time-varying stimuli. The data are correlated over time and a major effort is to develop a class of models, called inhomogeneous Markov interval (IMI) process models, which can adequately represent the data.Statistical methods for simple statistical models with a small number of parameters are well established.These models often do not provide an adequate representation of the phenomenon under investigation.Currently, scientists are deluged with huge volumes of high quality data. These data afford scientists the opportunity to use very complex models that more faithfully reflect reality. The researchers involved in this proposal are developing methodology and theory for analyzing data from these complex models. The methods are very general but they are being developed for applications in Astrophysics, Genetics and Neuroscience.