Informed importance tempering (IIT) is an easy-to-implement MCMC algorithm that can be seen as an extension of the familiar Metropolis-Hastings algorithm with the special feature that informed proposals are always accepted, and which was shown in Zhou and Smith (2022) to converge much more quickly in some common circumstances. This work develops a new, comprehensive guide to the use of IIT in many situations. First, we propose two IIT schemes that run faster than existing informed MCMC methods on discrete spaces by not requiring the posterior evaluation of all neighboring states. Second, we integrate IIT with other MCMC techniques, including simulated tempering, pseudo-marginal and multiple-try methods (on general state spaces), which have been conventionally implemented as Metropolis-Hastings schemes and can suffer from low acceptance rates. The use of IIT allows us to always accept proposals and brings about new opportunities for optimizing the sampler which are not possible under the Metropolis-Hastings framework. Numerical examples illustrating our findings are provided for each proposed algorithm, and a general theory on the complexity of IIT methods is developed.

翻译：知情重要性调节（IIT）是一种易于实现的MCMC算法，可视为经典Metropolis-Hastings算法的扩展，其特殊之处在于知情提议总是被接受。Zhou与Smith（2022）已证明，在某些常见场景中该算法收敛速度显著加快。本文系统性地发展了IIT在多场景下的全新应用指南。首先，我们提出两种IIT方案，通过无需评估所有相邻状态的后验概率，在离散空间上实现比现有知情MCMC方法更快的运行速度。其次，我们将IIT与模拟调节、伪边际方法和多尝试方法（在一般状态空间上）等其他MCMC技术相融合——这些传统上以Metropolis-Hastings方案实现的技术常面临低接受率问题。IIT的使用允许我们始终接受提议，并带来了在Metropolis-Hastings框架下无法实现的采样器优化新机遇。本文为每种算法提供数值实例验证发现，并建立了关于IIT方法复杂性的通用理论。