Beyond accept-reject sampling

Abstract

We propose a new estimator for estimating a quantity μ via Monte Carlo simulations, where μ=∫ƒ dP and P is the target probability measure. The new estimator outperforms the usual accept-reject algorithm in terms of reducing the variance. Properties of the estimator are derived. A new Rao-Blackwellised version of the estimator is also produced, but this version requires enormous computing time. Numerical results are provided.