Based on the algorithm Informed Importance Tempering (IIT) proposed by Li et al. (2023) we propose an algorithm that uses an adaptive bounded balancing function. We argue why implementing parallel tempering where each replica uses a rejection free MCMC algorithm can be inefficient in high dimensional spaces and show how the proposed adaptive algorithm can overcome these computational inefficiencies. We present two equivalent versions of the adaptive algorithm (A-IIT and SS-IIT) and establish that both have the same limiting distribution, making either suitable for use within a parallel tempering framework. To evaluate performance, we benchmark the adaptive algorithm against several MCMC methods: IIT, Rejection free Metropolis-Hastings (RF-MH) and RF-MH using a multiplicity list. Simulation results demonstrate that Adaptive IIT identifies high-probability states more efficiently than these competing algorithms in high-dimensional binary spaces with multiple modes.

翻译：基于Li等人（2023）提出的Informed Importance Tempering（IIT）算法，我们提出了一种使用自适应有界平衡函数的算法。我们论证了在高维空间中，每个副本均使用无拒绝MCMC算法的并行回火实现可能效率低下，并展示了所提出的自适应算法如何克服这些计算效率问题。我们提出了自适应算法的两个等价版本（A-IIT和SS-IIT），并证明两者具有相同的极限分布，因此均适用于并行回火框架。为评估性能，我们将自适应算法与多种MCMC方法进行基准测试：IIT、无拒绝Metropolis-Hastings（RF-MH）以及使用多重性列表的RF-MH。仿真结果表明，在多峰的高维二元空间中，自适应IIT在识别高概率状态方面比这些竞争算法更高效。