Optimality in importance sampling: a gentle survey

• URL: http://arxiv.org/abs/2502.07396v1
• Date: Tue, 11 Feb 2025 09:23:26 GMT
• Title: Optimality in importance sampling: a gentle survey
• Authors: Fernando Llorente, Luca Martino,
• Abstract summary: The performance of Monte Carlo sampling methods relies on the crucial choice of a proposal density. This work is an exhaustive review around the concept of optimality in importance sampling.
• Score: 50.79602839359522
• License:
• 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.

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