In this paper we describe a DSMC algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes.This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases.By numerical experiments we study the sensitivity of the algorithm to the number of simulation particles and to the discretization of the velocity space, when approximating the steady state distribution.