MCMC for multi-modal distributions

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.