Accept-Reject sampling Method (并非近似贝叶斯计算采样)

The Accept-Reject method is a classical sampling method which allows one to sample from a distribution which is difficult or impossible to simulate by an inverse transformation. Instead, draws are taken from an instrumental density and accepted with a carefully chosen probability. The resulting draw is a draw from the target density.

Accept-Reject Algorithm

The objective is to sample from a target density , where ,  is the unnormalized target density, and  the potentially unknown normalizing constant. Suppose that we can sample from another density  and that there exists a constant  such that  for all . To obtain a draw from :

1. Draw a candidate  from  and  from , the uniform distribution on the interval .
2. If , return .
3. Otherwise, return to 1.

The expected number of iterations required to accept a draw is . To ensure efficiency, the optimal choice of  is:

References

• Chib, S. and E. Greenberg (1995). Understanding the Metropolis Hastings Algorithm. American Statistical Journal 49, 327–335.

• Robert, C.P., and G. Casella (2004). Monte Carlo Statistical Methods, Second Edition. New York: Springer.