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.

KEY WORDS: Chi-square distance, Effective sample size; Importance sampling; Rejection control; Rejection sampling.

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