Optimality in Noisy Importance Sampling
This work addresses a specific issue in statistical estimation for researchers in computational statistics, but it appears incremental as it builds on existing noisy IS frameworks.
The paper tackles the problem of importance sampling with noisy evaluations of the target density by deriving optimal proposal densities that incorporate noise variance information, proposing points in higher-noise regions to improve estimator performance.
In this work, we analyze the noisy importance sampling (IS), i.e., IS working with noisy evaluations of the target density. We present the general framework and derive optimal proposal densities for noisy IS estimators. The optimal proposals incorporate the information of the variance of the noisy realizations, proposing points in regions where the noise power is higher. We also compare the use of the optimal proposals with previous optimality approaches considered in a noisy IS framework.