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Paper No. 07-3

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JE Griffin

The Ornstein-Ulhenbeck Dirichlet Process and other time-varying processes for Bayesian nonparametric inference

Abstract: This paper introduces a new class of time-varying, meaure-valued stochastic processes for Bayesian nonparametric inference. The class of priors generalizes the normalized random measure (Kingman 1975) construction for static problems. The unnormalized measure on any measureable set follows an Ornstein-Uhlenbeck process as described by Barndorff-Nielsen and Shephard (2001). Some properties of the normalized measure are investigated. A particle filter and MCMC schemes are described for inference. The methods are applied to an example in the modelling of financial data.