Rejection Sampling Schemes for Simulating from Arbitrary Probability Densities

Abstract

Simulating random variates from arbitrary non-normalized probability densities, very often they do not have familiar forms, is an increasingly important requirement in many different fields, especially in Bayesian statistics. Accept-reject algorithm is one of the commonly used methods to simulate random variates from such densities but restriction on choosing proposal density under this framework (heavier tails than the target density) limits its applicability to a larger extent. On the other hand, Markov Chain Monte Carlo (MCMC) method can choose proposal density arbitrary which makes this method applicable to a larger class of target densities5. In addition to MCMC method, a more general widely used method known as ratio-of-uniforms (RoU) which requires only two uniform variates to simulate one variates from such densities. However, no empirical comparison among these methods for simulating random variates from such densities was seen in the literature. In this paper, we limit our study only to MCMC and RoU methods to simulate random variates from such densities. Following the generation of random variates from such densities using these two methods, we compare the performance of these two methods based on quality of the generated samples. Finally, we conclude that RoU method performs better than MCMC method as far as quality of the generated sample (randomness) and computational cost are concerned.