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University of Cambridge > Talks.cam > Statistics Reading Group > Ferguson's 1973 paper on the Dirichlet process

## Ferguson's 1973 paper on the Dirichlet processAdd to your list(s) Download to your calendar using vCal - University of Cambridge
- Wednesday 25 February 2009, 16:30-17:30
- MR5, CMS.
If you have a question about this talk, please contact Richard Samworth. In 1973, Ferguson proposed to perform nonparametric estimation in a Bayesian framework by defining a prior distribution on an infinite-dimensional parameter space (the set of probability measures over a given domain). When applied to a finite set of observations, only a finite number out of the infinitely many degrees of freedom is used to explain the data, which accounts for the term “nonparametric”. The prior model is constructed as a stochastic process, with Dirichlet marginals and pathes in the set of probability measures over a separable metric space, that Ferguson called a “Dirichlet process”. His estimation model has a conjugate form with a closed-form solution for the posterior parameters, which mimics the conjugate posteriors of the Dirichlet marginals under a multinomial sampling model. Measures drawn at random from the Dirichlet process are a.s. discrete. I will review Ferguson’s construction and his application of the model to sample observations. I also intend to briefly discuss the two major lines of research which developed from Ferguson’s paper: One that attempts to overcome the model’s discreteness in order to construct “universal” priors, and one that exploits discreteness to generalize the notion of finite mixtures and related models. Article: http://www.ams.org/mathscinet-getitem?mr=350949 TS Ferguson, “A Bayesian analysis of some nonparametric problems” Ann. Statist. 1 (1973), 209—230. This talk is part of the Statistics Reading Group series. ## This talk is included in these lists:- All CMS events
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