Importance sampling (IS) is a Monte Carlo technique that relies on weighted samples, simulated from a proposal distribution, to estimate intractable integrals. The quality of the estimators improves with the number of samples. However, for achieving a desired quality of estimation, the required number of samples is unknown, and depends on the quantity of interest, the estimator, and the chosen proposal. We present a sequential stopping rule that terminates simulation when the overall variability in estimation is relatively small. The proposed methodology closely connects to the idea of an effective sample size in IS and overcomes crucial shortcomings of existing metrics, e.g., it acknowledges multivariate estimation problems. Our stopping rule retains asymptotic guarantees and provides users a clear guideline on when to stop the simulation in IS.
翻译:重要性取样(IS)是一种蒙特卡洛技术,它依靠加权样品,根据建议分发情况模拟,估计难以处理的积分;估计者的质量随着样品数量的增加而提高;然而,为了达到预期的估计质量,所需样品的数量并不为人所知,取决于利息的数量、估计者以及选定的提议。我们提出了一个连续停止规则,在估计的总体变异性相对较小时终止模拟。拟议方法与估计中有效抽样规模的概念密切相关,并克服现有指标的重大缺陷,例如,它承认多变量估计问题。我们的停止规则保留了无损保证,并为用户提供了在何时停止IS模拟的明确准则。