A stochastic diffusion process for Lochner's generalized Dirichlet distribution

A Stochastic Diffusion Process for the Dirichlet Distribution

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a couplednonlinear diffusionprocess is required: theWiener processes in the equivalent systemof stochastic differential equations are multipli...

Lecture 24 : Dirichlet distribution and Dirichlet Process

Generalized Spatial Dirichlet Process Models

By JASON A. DUAN Institute of Statistics and Decision Sciences at Duke University, Durham, North Carolina, 27708-0251, U.S.A. [email protected] MICHELE GUINDANI Istituto di Metodi Quantitativi, Università Bocconi, 20136, Milano, Italy [email protected] and ALAN E. GELFAND Institute of Statistics and Decision Sciences at Duke University, Durham, North Carolina, 27708-0251, U.S.A. ...

Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process

The two parameter Poisson-Dirichlet distribution PD(α, θ) is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman’s Poisson-Dirichlet distribution. The two parameter Dirichlet process Πα,θ,ν0 is the law of a pure atomic random measure with masses following the two parameter Poisson-Dirichlet distribution. In this article we focus on the cons...

Dirichlet Process Mixtures of Generalized Linear Models

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new class of methods for nonparametric regression. Given a data set of input-response pairs, the DP-GLM produces a global model of the joint distribution through a mixture of local generalized linear models. DP-GLMs allow both continuous and categorical inputs, and can model the same class of responses that can be mo...