Safe and Effective Importance Sampling

作者：Art B. Owen, Yi Zhou · 发表于：Journal of the American Statistical Association · 年份：2000 · DOI：10.1080/01621459.2000.10473909 · 被引用次数：365 · 研究领域：Mathematical Approximation and Integration、Probabilistic and Robust Engineering Design、Bayesian Methods and Mixture Models

We present two improvements on the technique of importance sampling. First, we show that importance sampling from a mixture of densities, using those densities as control variates, results in a useful upper bound on the asymptotic variance. That bound is a small multiple of the asymptotic variance of importance sampling from the best single component density. This allows one to benefit from the great variance reductions obtainable by importance sampling, while protecting against the equally great variance increases that might take the practitioner by surprise. The second improvement is to show how importance sampling from two or more densities can be used to approach a zero sampling variance even for integrands that take both positive and negative values.