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：蒙特卡洛采样方法的性能依赖于一个关键的选择：提议密度。最优性这一概念对于在蒙特卡洛方案中设计合适的提议密度自适应过程至关重要。本文围绕重要性采样中的最优性概念进行了详尽的综述。文中描述并分析了多个框架，例如用于模型选择的边际似然近似、多重提议密度的使用、一系列退火后验分布，以及包含噪声的场景——例如在近似贝叶斯计算（ABC）和强化学习中的应用等。文中还提供了一些理论与实证比较。