A rejection sampling scheme for posterior probability distributions via the ratio-of-uniforms method

Accept/reject sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. The main limitation to the use of RS is the need to find an adequate upper bound for the ratio of the target pdf over the proposal pdf from which the samples are generated. There are no general methods to analytically find this bound, except when the target pdf is log-concave. In this paper we introduce a novel procedure using the ratio of uniforms method to efficiently perform rejection sampling for a large class of target densities. The candidate samples are generated using only two independent uniform random variables. In order to illustrate the application of the proposed technique, we provide a numerical example.