  The beta process has recently been widely used as a nonparametric prior for
different models in machine learning, including latent feature models. In this
paper, we prove the asymptotic consistency of the finite dimensional
approximation of the beta process due to Paisley \& Carin (2009). In addition,
we derive an almost sure approximation of the beta process. This approximation
provides a direct method to efficiently simulate the beta process. A simulated
example, illustrating the work of the method and comparing its performance to
several existing algorithms, is also included.
