Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captured by the approximating distribution, in which case more stable estimates can be obtained by modifying extreme importance ratios. We present a new method for stabilizing importance weights using a generalized Pareto distribution fit to the upper tail of the distribution of the simulated importance ratios. The method, which empirically performs better than existing methods for stabilizing importance sampling estimates, includes stabilized effective sample size estimates, Monte Carlo error estimates, and convergence diagnostics. The presented Pareto $\hat{k}$ finite sample convergence rate diagnostic is useful for any Monte Carlo estimator.

翻译：重要性加权是一种通用的调整蒙特卡洛积分的方法，用于纠正从错误分布进行采样所带来的偏差，但当重要性比率具有重右尾时，所得估计可能具有高度变异性。当目标分布中存在近似分布未能良好捕捉的方面时，这种情况经常发生，此时通过修改极端重要性比率可以获得更稳定的估计。我们提出了一种新的方法，使用广义帕累托分布对模拟重要性比率分布的上尾进行拟合，从而稳定重要性权重。该方法在稳定重要性采样估计方面经验性地优于现有方法，并包括稳定的有效样本量估计、蒙特卡洛误差估计以及收敛诊断。所提出的帕累托 $\hat{k}$ 有限样本收敛速率诊断方法适用于任何蒙特卡洛估计量。