On a rapid simulation of the Dirichlet process

We describe a simple, yet efficient, procedure for approximating the Lévy measure of a Gamma(α,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. This approximation is written 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 significant improvement.