Pareto Smoothed Importance Sampling
This addresses a specific issue in Monte Carlo integration for statisticians and researchers, offering incremental improvements over prior stabilization techniques.
The paper tackles the problem of high variability in importance sampling estimates when importance ratios have heavy tails, and presents a new method using a generalized Pareto distribution to stabilize weights, which empirically outperforms existing methods and includes diagnostics for effective sample size, Monte Carlo error, and convergence.
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.