Hamiltonian Monte Carlo (HMC) methods are widely used to draw samples from unnormalized target densities due to high efficiency and favorable scalability with respect to increasing space dimensions. However, HMC struggles when the target distribution is multimodal, because the maximum increase in the potential energy function (i.e., the negative log density function) along the simulated path is bounded by the initial kinetic energy, which follows a half of the $\chi_d^2$ distribution, where d is the space dimension. In this paper, we develop a Hamiltonian Monte Carlo method where the constructed paths can travel across high potential energy barriers. This method does not require the modes of the target distribution to be known in advance. Our approach enables frequent jumps between the isolated modes of the target density by continuously varying the mass of the simulated particle while the Hamiltonian path is constructed. Thus, this method can be considered as a combination of HMC and the tempered transitions method. Compared to other tempering methods, our method has a distinctive advantage in the Gibbs sampler settings, where the target distribution changes at each step. We develop a practical tuning strategy for our method and demonstrate that it can construct globally mixing Markov chains targeting high-dimensional, multimodal distributions, using mixtures of normals and a sensor network localization problem.

翻译：Hamilton Monte Carlo (HMC) 方法被广泛用于从未规范的目标密度中提取样本,因为效率高,且在增加的空间尺寸方面可进行有利的缩放。然而,HMC在目标分布为多式联运时会挣扎,因为模拟路径上潜在能量功能的最大增加(即负日志密度功能)受初始动能的约束,而最初动力能量的提高(即在建造汉密尔顿路径时,潜在微粒质量持续变化,即负日志密度功能)受模拟路径上潜在能量的最大增加的约束。因此,这种方法可以被视为HMC和缓冲过渡方法的结合。与其它调和方法相比,我们的方法在Gibs采样器环境中有着独特的优势,在每一步骤上的目标分布变化并不要求目标分布模式为人所熟知。我们的方法使得目标密度的孤立模式之间经常发生跳跃。我们的方法能够通过在建造汉密尔顿路径时不断改变模拟粒子质量。因此,这种方法可以被视为HMC和缓冲过渡方法的结合。与其他调和方法相比,我们的方法在GIS 采样器设置中具有独特的优势,在每一步骤上的目标分布变化。这种方法不需要事先知道目标分布模式的模式的模式的模式。我们制定一个针对全球的正常的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型。我们为全球模型的模型。