Bayesian Statistics: An Introduction, 4th Edition

9.5 Rejection sampling

9.5.1 Description

An important method which does not make use of Markov chain methods but which helps to introduce the Metropolis–Hastings algorithm is rejection sampling or acceptance-rejection sampling. This is a method for use in connection with a density in the case where the normalizing constant K is quite possibly unknown, which, as remarked at the beginning of this chapter, is a typical situation occurring in connection with posterior distributions in Bayesian statistics. To use this method, we need to assume that there is a candidate density from which we can simulate samples and a constant c such that . Then, to obtain a random variable with density we proceed as follows:

1. Generate a variate Y from the density ;

2. Generate a value which is uniformly ...