Optimality in importance sampling: a gentle survey
Computation
2026-02-24 v2 Computational Engineering, Finance, and Science
Machine Learning
Abstract
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This work is an exhaustive review around the concept of optimality in importance sampling. Several frameworks are described and analyzed, such as the marginal likelihood approximation for model selection, the use of multiple proposal densities, a sequence of tempered posteriors, and noisy scenarios including the applications to approximate Bayesian computation (ABC) and reinforcement learning, to name a few. Some theoretical and empirical comparisons are also provided.
Cite
@article{arxiv.2502.07396,
title = {Optimality in importance sampling: a gentle survey},
author = {Fernando Llorente and Luca Martino},
journal= {arXiv preprint arXiv:2502.07396},
year = {2026}
}