Bayesian data analysis is widely used across many disciplines, and representative examples in materials science include spectral analysis and sparse modeling. In such applications, the underlying models often become complex and yield multimodal posterior distributions, making efficient sampling from multimodal distributions essential. Replica exchange Monte Carlo has been commonly employed for this purpose; however, its performance strongly depends on difficult parameter tuning, such as the design of the inverse temperature. In this study, we comparatively investigate sampling algorithms that require fewer tuning parameters for Bayesian data analysis in materials science. Specifically, we compare three approaches: non-reversible parallel tempering (NRPT), sequential Monte Carlo samplers (SMCS), and a newly proposed method, sequential exchange Monte Carlo (SEMC). Our results indicate that NRPT can require computational time for parameter tuning, while SMCS requires careful adjustment of the number of MCMC steps at each temperature level. In contrast, SEMC achieves robust convergence across a range of problem settings without additional tuning, demonstrating its practicality for Bayesian inference.

翻译：贝叶斯数据分析在众多学科中得到广泛应用，材料科学中的典型实例包括谱分析和稀疏建模。在此类应用中，底层模型往往变得复杂并产生多峰后验分布，因此从多峰分布中进行高效采样至关重要。副本交换蒙特卡洛方法常被用于此目的；然而其性能高度依赖于困难的参数调优，例如逆温度的设计。本研究针对材料科学中的贝叶斯数据分析，比较研究了需要较少调优参数的采样算法。具体而言，我们比较了三种方法：不可逆并行回火（NRPT）、序贯蒙特卡洛采样器（SMCS）以及新提出的序贯交换蒙特卡洛（SEMC）方法。研究结果表明，NRPT可能需要参数调优的计算时间，而SMCS需要在每个温度层级仔细调整MCMC步数。相比之下，SEMC在多种问题设置下均能实现稳健收敛且无需额外调优，证明了其在贝叶斯推断中的实用性。