Markov process techniques and asymptotics for the analysis of spatial and temporal data

用于空间和时间数据分析的马尔可夫过程技术和渐近法

• 批准号: 263899-2006
• 负责人: Balan, Raluca
• 金额: $ 1.17万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=395537
• 关键词: Markov; process; techniques; asymptotics; analysis

This program will focus on combining innovative techniques in modern statistics, including the analysis of longitudinal data and Bayesian nonparametric statistics, with fundamental research in probability theory and stochastic processes. a) The generalized estimation equation (GEE) approach is an extension of generalized linear models, which provides a semiparametric approach to longitudinal data analysis. This program will concentrate on issues related to the consistency and asymptotic normality of the regression parameter, when some of the responses are missing from the study. The use of the empirical likelihood method in this context constitutes a novel approach, which has the potential to generate new results that can be applied to a broad range of data situations. b) The construction of prior distributions on the space of all distribution functions, which have large support and analytically tractable posteriors is at the core of many investigations in modern statistics. Building on recent advances in this area, the present program will concentrate on issues related to the posterior consistency of the Markov prior, as well as its applications to censored data. c) This part of the research program will focus on the asymptotic behavior of various statistics associated to certain classes of self-normalized observations, which may describe the evolution of systems depending on many parameters. This will constitute an important contribution in a promising new area of fundamental research. d) The solution of a stochastic partial differential equation (SPDE) is typically a process that behaves randomly in time and space. In many applications, it is important to understand when the solution process possesses the germ Markov property, which requires that the "future" evolution of the process be independent of its past given the present status, for a given time-space region. The goal of this program will be to examine a large class of SPDE's whose solution processes possess the germ Markov property.

该计划将侧重于结合现代统计学的创新技术，包括纵向数据和贝叶斯非参数统计的分析，以及概率论和随机过程的基础研究。a）广义估计方程（GEE）方法是广义线性模型的扩展，它为纵向数据分析提供了半参数方法。本程序将集中讨论当研究中缺少某些响应时，回归参数的一致性和渐近正态性相关问题。在这种情况下，使用经验似然法构成了一种新的方法，它有可能产生新的结果，可以应用于广泛的数据情况。B）在所有分布函数的空间上构造先验分布，它具有大的支持度和易于分析的后验，是现代统计学中许多研究的核心。在这一领域的最新进展的基础上，本计划将集中在与马尔可夫先验的后验一致性相关的问题，以及它在删失数据中的应用。c）研究计划的这一部分将侧重于与某些类别的自归一化观测相关的各种统计量的渐近行为，这些统计量可以描述依赖于许多参数的系统的演化。这将构成一个有前途的基础研究新领域的重要贡献。d）随机偏微分方程（SPDE）的解通常是在时间和空间上随机行为的过程。在许多应用中，重要的是要了解解过程何时具有芽马尔可夫性质，这要求过程的“未来”演化在给定的时空区域内独立于其过去。这个程序的目标将是检查一大类的SPDE的解决方案具有芽马尔可夫财产。