Matrix Dirichlet processes

TL;DR

This paper introduces matrix Dirichlet processes, exploring their properties and models via diffusion operators, boundary equations, and realizations through Brownian motion, polar decomposition, and Wishart processes.

Contribution

It provides new models and a detailed analysis of matrix Dirichlet processes using advanced mathematical tools and various realizations.

Findings

Describes Dirichlet processes on the simplex.

Provides models via Brownian motion and Wishart processes.

Connects matrix Dirichlet processes with boundary equations.

Abstract

Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the method of boundary equations, we describe Dirichlet processes on the simplex and provide two models of matrix Dirichlet processes, which can be realized by various projections, through the Brownian motion on the special unitary group, the polar decomposition of complex matrices and also through Wishart processes.