Importance sampling (IS) is an important technique to reduce the estimation variance in Monte Carlo simulations. In many practical problems, however, the use of IS method may result in unbounded variance, and thus fail to provide reliable estimates. To address the issue, we propose a method which can prevent the risk of unbounded variance; the proposed method performs the standard IS for the integral of interest in a region only in which the IS weight is bounded and use the result as an approximation to the original integral. It can be verified that the resulting estimator has a finite variance. Moreover, we also provide a normality test based method to identify the region with bounded IS weight (termed as the safe region) from the samples drawn from the standard IS distribution. With numerical examples, we demonstrate that the proposed method can yield rather reliable estimate when the standard IS fails, and it also outperforms the defensive IS, a popular method to prevent unbounded variance.

中文翻译：

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一种用于方差减少的权重有界重要性抽样方法

重要性采样 (IS) 是减少 Monte Carlo 模拟中估计方差的重要技术。然而，在许多实际问题中，使用 IS 方法可能会导致无界方差，从而无法提供可靠的估计。为了解决这个问题，我们提出了一种可以防止无界方差风险的方法；所提出的方法仅在 IS 权重有界的区域中对感兴趣的积分执行标准 IS，并将结果用作原始积分的近似值。可以验证所得估计量具有有限方差。此外，我们还提供了一种基于正态性检验的方法，以从标准 IS 分布中抽取的样本中识别具有有界 IS 权重的区域（称为安全区域）。用数值例子，