Another Look at Rejection Sampling Through Importance Sampling

We provide a different view of rejection sampling by putting it in the framework of importance sampling. When rejection sampling with an envelope function g is viewed as a special importance sampling algorithm, we show that it is inferior to the importance sampling algorithm with g as the proposal distribution in terms of the Chi-square distance between the proposal distribution and the target distribution. Similar conclusions are drawn for comparing rejection control with importance sampling. Some key words: Chi-square distance, Effective sample size; Importance sampling; Rejection control; Rejection sampling. Yuguo Chen is with Institute of Statistics and Decision Sciences, Duke University, Durham, NC 27708, USA (e-mail: [email protected]). This research was partly supported by the National Science Foundation grant DMS0203762.