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.

翻译：蒙特卡罗采样方法的性能依赖于提议密度的关键选择。最优性概念对于在蒙特卡罗方案中设计合适的提议密度自适应过程至关重要。本文是对重要性采样中最优性概念的全面综述。我们描述并分析了多种框架，例如用于模型选择的边际似然近似、多个提议密度的使用、一系列退火后验分布，以及包含近似贝叶斯计算（ABC）和强化学习等应用在内的噪声场景。此外，还提供了一些理论和实证比较。