Computationally Tractable Estimation Methods for Markov Processes

马尔可夫过程的可计算处理估计方法

• 批准号: 9704648
• 负责人: Katherine Ensor
• 金额: $ 6.45万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-01 至 2001-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704648&HistoricalAwards=false
• 关键词: Computationally; Tractable; Estimation; Methods; Markov

NSF DMS-9704648 Katherine Bennett Ensor Markov process theory provides a rich analytic and probablistic structure which is intrinsically natural from a modelling perspective. Much of the literature on inference for continuous-time Markov processes assumes that the process has been observed continuously over some time interval. However, in practice, many of the data sets available involve observing only discrete ``snapshots'' of the process. Existing theory on parameter estimation in this setting often results in computationally prohibitive methodologies. This research addresses the issue of computationally tractable parameter estimation for discretely observed continuous-time Markov processes. Many of the results utilize Monte Carlo simulation to achieve tractability. The second fundamental question examined in this research is that of error propagation through a stochastic system. When the output performance measure of the stochastic system cannot be evaluated in closed form the output measure is simulated from the modelled system. To address this situation, the investigators develop estimators and their sampling properties for functionals of the stochastic system. Statistical models have always proven a powerful tool for purposes of modelling, understanding and predicting complex systems. This research advances the frontier of statistical models for dependent observations. For example, the statistical methods of this research are applicable to the diverse areas of modelling levels of pollutants and contaminants in air, soil and water which evolve over time and/or space; forecasting changes in the stock market; and predicting or assessing demand for the development of an optimal communications network. The use of statistical models for purposes of modelling complex systems has been limited in the past due to the state of computing power; a state which has certainly improved in recent years. In this research, the investigators develop a framework for practical implementation of advanced statistical methodologies which capitalizes fully on the high performance computing available today. The research addresses the issue of modelling under partially observed information. For example, the electrical or computer engineer may use such models to assess network status when only partial information is available on the state of the system; in predicting air quality for a given region, observations of pollutant levels are made at sites irregularly located over the region and often at irregular points in time. The theoretical constructs necessary to implement the models in the more common scenario when only partial information is available are presented. Additionally, this research involves error assessment of the predictions or output performance measure of an estimated complex system again capitalizing on the availability of high powered computing.

NSF DMS-9704648凯瑟琳班尼特恩索尔 马尔可夫过程理论提供了丰富的分析和概率结构，从建模的角度来看，这是本质上自然的。 许多关于连续时间马尔可夫过程的推理的文献都假设该过程在某个时间间隔内被连续观察。 然而，在实践中，许多现有的数据集只涉及观察过程的离散"快照“。 现有的理论参数估计在这种情况下，往往会导致计算禁止的方法。 本研究针对离散观测连续时间马氏过程的参数估计问题，提出一种计算上易于处理的参数估计方法。 许多结果利用蒙特卡罗模拟来实现易处理性。 在这项研究中检查的第二个基本问题是通过随机系统的误差传播。 当随机系统的输出性能指标不能以封闭形式评估时，输出指标由建模系统模拟。 为了解决这种情况下，调查人员开发的随机系统的泛函估计和他们的抽样性能。 统计模型一直被证明是建模，理解和预测复杂系统的强大工具。 这项研究推进了相关观测统计模型的前沿。 例如，这项研究的统计方法适用于模拟空气、土壤和水中污染物和污染物水平随时间和/或空间的变化;预测股票市场的变化;预测或评估发展最佳通信网络的需求等不同领域。 过去，由于计算能力的状况，使用统计模型对复杂系统进行建模受到限制;近年来，这种状况肯定有所改善。 在这项研究中，研究人员开发了一个框架，用于实际实施先进的统计方法，充分利用当今可用的高性能计算。该研究解决了部分观测信息下的建模问题。 例如，电气或计算机工程师可以使用这样的模型来评估网络状态时，只有部分信息是可用的状态的系统;在预测空气质量为一个给定的区域，污染物水平的观察是在不规则的位置在该地区，往往在不规则的时间点。 必要的理论结构，以实现在更常见的情况下，只有部分信息是可用的模型。 此外，这项研究涉及的预测或估计的复杂系统的输出性能测量的错误评估再次利用高性能计算的可用性。