We explain the fundamental challenges of sampling from multimodal distributions, particularly for high-dimensional problems. We present the major types of MCMC algorithms that are designed for this purpose, including parallel tempering, mode jumping and Wang-Landau, as well as several state-of-the-art approaches that have recently been proposed. We demonstrate these methods using both synthetic and real-world examples of multimodal distributions with discrete or continuous state spaces.

翻译：本文阐述了从多模态分布中采样的基本挑战，尤其针对高维问题。我们介绍了为此目的设计的主要类型MCMC算法，包括并行回火、模态跳跃和Wang-Landau方法，以及近期提出的若干前沿方法。我们通过离散或连续状态空间的多模态分布合成实例与真实案例，对这些方法进行了演示。