Random Measures: Asymptotics, Bayesian Inference, and Stochastic Dynamics

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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.