POWRE: Dynamical MCMC Methods With Applications to Continuous Time Differential Equation Models

POWRE：动态 MCMC 方法及其在连续时间微分方程模型中的应用

• 批准号: 9805598
• 负责人: Osnat Stramer
• 金额: $ 7.5万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-15 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9805598&HistoricalAwards=false
• 关键词: POWRE; Dynamical; MCMC; Methods; Applications

9805598 Stramer Many physical systems are described by continuous-time models (diffusions) which incorporate the variability and randomness that occurs in the real world. The PI will carry out research on two different aspects of such systems: the first enables the use of diffusions to give more efficient computing methods in simulation, and the second leads to better inference of the properties of systems. Part I: Development of new Markov Chain Monte Carlo (MCMC) algorithms for efficient computation of a given high-dimensional density pi which is known up to a factor of proportionality. These new algorithms will be based on multi-dimensional diffusion approximations. The basic idea is to find, for a given probability density pi, a class of diffusion processes (continuous-time, continuous sample-path Markov chains) which have pi as an equilibrium distribution. It is expected that the proposed new MCMC algorithms will speed up simulations of a broad class of distributions pi. Part II: Contribution to statistical inference in non-linear continuous time modeling. It is often appropriate to model the time evolution of dynamic systems by using continuous time stochastic processes whose dynamics are characterized by stochastic differential equations. It is proposed to employ a Bayesian approach for model estimation based on MCMC methods. New simulation techniques for estimating the posterior distribution for a broad class of non-linear Continuous time models will be studied. The existing estimation methods in the literature depend on the length of the interval between two observations and hence Metropolis sub-algorithms for augmenting the data set will be studied. This research is expected to provide a new approach for inference in a broad class of continuous time models. This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).

9805598 Stramer许多物理系统都是由连续时间模型（扩散）描述的，它包含了真实的世界中发生的可变性和随机性。 PI将对此类系统的两个不同方面进行研究：第一个方面使扩散的使用能够在模拟中提供更有效的计算方法，第二个方面导致更好地推断系统的属性。 第一部分：开发新的马尔可夫链蒙特卡罗（MCMC）算法，用于有效计算已知比例因子的给定高维密度pi。 这些新的算法将基于多维扩散近似。 其基本思想是，对于给定的概率密度pi，找到一类扩散过程（连续时间，连续样本路径马尔可夫链），其中pi作为平衡分布。 预计所提出的新MCMC算法将加快对广泛的一类分布Pi的模拟。 第二部分：对非线性连续时间建模中统计推断的贡献。 用连续时间随机过程来模拟动态系统的时间演化往往是合适的，其动力学特征是随机微分方程。 提出了采用贝叶斯方法进行基于MCMC方法的模型估计。 新的模拟技术，估计后验分布的一个广泛的类的非线性连续时间模型将进行研究。 文献中现有的估计方法依赖于两个观测值之间的间隔长度，因此将研究用于扩充数据集的大都会子算法。 该研究有望为大类连续时间模型的推理提供一种新的方法。 该项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）共同支持。