Sampling from high-dimensional, multimodal distributions using automatically tuned, tempered Hamiltonian Monte Carlo
提出一种结合调温与哈密顿蒙特卡洛的方法，通过模拟时变哈密顿动力学自动调温，高效采样高维强多模态分布，在贝叶斯推断中表现优于自适应并行调温等方法。
Abstract Hamiltonian Monte Carlo (HMC) is widely used for sampling from high-dimensional target distributions with densities known up to proportionality. While HMC exhibits favourable scaling properties in high dimensions, it struggles with strongly multimodal distributions. Tempering methods are commonly used to address multimodality, but they can be difficult to tune, especially in high-dimensional settings. In this study, we propose a method that combines tempering with HMC to enable efficient sampling from high-dimensional, strongly multimodal distributions. Our approach simulates the dynamics of a time-varying Hamiltonian in which the temperature increases and then decreases over time. In the first phase, the simulated trajectory gradually explores low-density regions farther from the mode; the second phase guides it back towards a local mode. We develop efficient tuning strategies based on a time-scale transformation under which the Hamiltonian becomes approximately stationary. This leads to a tempered Hamiltonian Monte Carlo (THMC) algorithm with automatic tuning. We demonstrate numerically that our method scales more effectively with dimension than adaptive parallel tempering and tempered sequential Monte Carlo. Finally, we apply our THMC to sample from strongly multimodal posterior distributions arising in Bayesian inference.