AbstractIn recent years, Bayesian nonparametric statistics has received extraordinary attention. The beta‐Stacy process, a generalization of the Dirichlet process, is a fundamental tool in studying Bayesian nonparametric statistics. In this article, we derive a simple, yet efficient, way to simulate the beta‐Stacy process. We compare the efficiency of the new approximation to several other well‐known approximations, and we demonstrate a significant improvement. Using the Kolmogorov distance and samples from the beta‐Stacy process, a Bayesian nonparametric goodness of fit test is proposed. The proposed test is very general in the sense that it can be applied to censored and non‐censored observations. Some illustrative examples are included. 41: 466–487; 2013 © 2013 Statistical Society of Canada