On a Rapid Simulation of the Dirichlet Process

TL;DR

This paper introduces a fast and accurate simulation method for the Dirichlet process using a novel approximation of the gamma distribution's Lévy measure, significantly improving efficiency over existing methods.

Contribution

The authors propose a new finite sum-representation for the Dirichlet process that converges almost surely and outperforms previous approximation techniques.

Findings

The new approximation is computationally more efficient.

It provides a nearly exact simulation of the Dirichlet process.

The method shows substantial improvement over existing approximations.

Abstract

We describe a simple and efficient procedure for approximating the L\'evy measure of a $\text{Gamma}(\alpha,1)$ random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process based on arrivals of a homogeneous Poisson process. We compare the efficiency of our approximation to several other well known approximations of the Dirichlet process and demonstrate a substantial improvement.