Complex Statistical Models: Theory and Methodology for Scientific Applications

复杂统计模型：科学应用的理论与方法。Kassand Kathryn Roeder摘要该项目旨在为高度复杂的，可能是无限维的模型开发统计理论和方法。 虽然方法和理论将是相当普遍的，我们将进行研究的背景下，三个科学合作。 第一个是“描述宇宙中的大尺度结构”，这是一个与天体物理学家和计算机科学家的联合项目。 主要的统计挑战是非参数密度估计和聚类，受到高度非线性约束。第二个项目是“通过基因组控制定位疾病基因”。我们的目标是定位病例（患病受试者）中比对照组具有更多遗传相似性的基因组区域。这些区域是包含疾病基因的候选者。以严格的统计方式找到这些区域需要测试大量的假设。 我们将扩展和发展多假设检验的最新技术。第三个项目是“模拟神经元放电模式”。目标是构建和拟合神经元放电模式的模型，称为尖峰序列。这些数据包括许多神经元的同时电压记录，这些神经元受到随时间变化的刺激。数据是随着时间的推移而相关的，主要的努力是开发一类模型，称为非齐次马尔可夫间隔（IMI）过程模型，它可以充分地表示数据。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。这些模型通常不能充分地表示所研究的现象。目前，科学家们被大量高质量的数据淹没。这些数据为科学家提供了使用更忠实地反映现实的非常复杂的模型的机会。参与这项提案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。这些方法是非常普遍的，但他们正在开发应用在天体物理学，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.