A principled stopping rule for importance sampling

Importance sampling (IS) is a Monte Carlo technique that relies on weighted samples, simulated from proposal distribution, to estimate intractable integrals. The quality of the estimators improves with number samples. However, for achieving desired estimation, required samples unknown and depends quantity interest, estimator, chosen proposal. We present sequential stopping rule terminates simulation when overall variability in estimation relatively small. proposed methodology closely connects idea an effective sample size IS overcomes crucial shortcomings existing metrics, e.g., it acknowledges multivariate problems. Our retains asymptotic guarantees provides users clear guideline stop IS.