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Sequential Monte Carlo in Random Environments

随机环境中的顺序蒙特卡罗

基本信息

批准号：
EP/K023330/1
负责人：
Nick Whiteley
金额：
$ 12.51万
依托单位：
University of Bristol
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2013
资助国家：
英国
起止时间：
2013 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FK023330%2F1
关键词：
Sequential Monte Carlo Random Environments

项目摘要

Statistical analysis of data sequences using complex, non-linear stochastic models is now practically feasible due to the availability of sequential Monte Carlo algorithms. These algorithms allow us to tackle the computational problems which arise when attempting to draw conclusions, inform decisions and make predictions on the basis of data sequences gathered from the world around us. However, despite their remarkable popularity, there is currently no precise, rigorous and general notion of long-run efficiency of these algorithms in the context of model calibration and comparison tasks, so there is no way to formally compare the performance of existing algorithms as the length of the data sequences grow, nor any clear way in which to devise new algorithms which are guaranteed to perform well in this regime. The increasing availability of long data records and recent uptake of sequential Monte Carlo in a variety of burgeoning scientific areas provides strong and immediate motivation for investigation of these matters.The objectives of the proposed research are to (A) develop a new theoretical and methodological framework in which to address notions of long-run efficiency of sequential Monte Carlo algorithms; and thereby (B) devise new algorithms which are guaranteed to remain practically useful as data sequences grow in length. These objectives are to be achieved through investigation of the subtle interplay between aspects of non-linear estimation, long-run data properties and stochastic simulation techniques in the probabilistic setting of a random environment. The ultimate purpose of the research is equip statistical scientists with a powerful suite of computational techniques with which to face the challenges of modern data analysis.

由于连续蒙特卡罗算法的可用性，使用复杂的非线性随机模型对数据序列进行统计分析现在实际上是可行的。这些算法使我们能够解决在试图根据从我们周围的世界收集的数据序列得出结论、做出决策和预测时出现的计算问题。然而，尽管它们非常受欢迎，但目前在模型校准和比较任务的背景下，这些算法的长期运行效率没有精确，严格和一般的概念，因此没有办法正式比较现有算法的性能，因为数据序列的长度增长，也没有任何明确的方法来设计保证在这种制度下表现良好的新算法。长时间数据记录的不断增加和最近在各种新兴科学领域中对序列蒙特卡罗算法的采用为这些问题的研究提供了强大而直接的动机。拟议研究的目标是（A）发展一个新的理论和方法框架，在其中解决序列蒙特卡罗算法的长期有效性的概念;并且由此（B）设计新的算法，当数据序列长度增长时，该算法保证保持实际有用。这些目标是通过调查非线性估计，长期数据属性和随机模拟技术在随机环境的概率设置方面之间的微妙的相互作用来实现的。该研究的最终目的是为统计科学家提供一套强大的计算技术，以应对现代数据分析的挑战。