Random Measures: Asymptotics, Bayesian Inference, and Stochastic Dynamics

随机测度是一个测度值随机元素。随机度量的集合成为一个度量值过程。在过去的三十年中，随机测量和测量值过程一直是概率论、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割、聚结、狄利克雷过程、棍断模型、弗莱明-维奥过程和各种瓮模型。他们研究的一个主要动机是对复杂的相互作用系统和相应的演化动力学进行建模。这一领域的深入研究已经在概率论和随机过程方面取得了许多理论进展，并在天体物理学、化学、通信、生态学、经济学、语言学、机器学习和群体遗传学等领域得到了大量应用。

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.