Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of layered adaptive importance sampling algorithms, which is a family of adaptive importance samplers where Markov chain Monte Carlo algorithms are employed to drive an underlying multiple importance sampling scheme. The modular nature of the layered adaptive importance sampling scheme allows for different possible implementations, yielding a variety of different performances and computational costs. In this work, we propose different enhancements of the classical layered adaptive importance sampling setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distributions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Different numerical experiments show the benefits of the proposed schemes, comparing with benchmark methods presented in the literature, and in several challenging scenarios.

蒙特卡罗抽样方法是在贝叶斯推理中逼近多维后验分布的复杂积分的标准程序。在这项工作中，我们专注于分层自适应重要性采样算法类，这是一个自适应重要性采样器家族，其中马尔可夫链蒙特卡罗算法用于驱动一个潜在的多重重要性抽样方案。分层自适应重要性采样方案的模块化特性允许不同的可能实现，产生各种不同的性能和计算成本。在这项工作中，我们提出了对经典分层自适应重要性采样设置的不同增强，以提高效率并降低上层和下层的计算成本。不同的变体解决了实际应用中出现的计算挑战，例如高度集中的后验分布。此外，我们引入了不同的策略来设计更便宜的方案，例如，回收上层生成的样本并在下层的最终估计器中使用它们。