Random Measures: Asymptotics, Bayesian Inference, and Stochastic Dynamics

随机测量：渐进、贝叶斯推理和随机动力学

• 批准号: RGPIN-2016-05400
• 负责人: Feng, Shui
• 金额: $ 1.6万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635948
• 关键词: Random; Measures; Asymptotics; Bayesian; Inference

A random measure is a measure-valued random element. A collection of random measures becomes a measure-valued process. Random measures and measure-valued processes have been highly active research subjects over the past three decades in probability theory, stochastic processes, and statistics. Some of the well studied models include random partitions, coalescent, Dirichlet process, stick breaking model, Fleming-Viot process, and various urn models. One main motivation for their study comes from modelling complex interacting systems and the corresponding evolving dynamics. Intensive studies in this area have led to many theoretical progresses in probability theory and stochastic processes, and plenty of applications in astrophysics, chemistry, communication, ecology, economics, linguistics, machine learning, and population genetics.

随机测度是测度值随机元。随机测度的集合成为测度值过程。随机测度和测度值过程在过去的三十年里一直是概率论、随机过程和统计学中非常活跃的研究课题。一些研究得很好的模型包括随机分配，聚结，狄利克雷过程，棒断裂模型，弗莱明-维奥特过程，和各种瓮模型。他们研究的一个主要动机来自于对复杂的相互作用系统和相应的演化动力学进行建模。在这一领域的深入研究导致了概率论和随机过程的许多理论进展，以及天体物理学，化学，通信，生态学，经济学，语言学，机器学习和人口遗传学的大量应用。