Title: Sequential-proposal Hamiltonian Monte Carlo with mass scaling for multimodal target distributions
Abstract: The Hamiltonian Monte Carlo (HMC) algorithm can be used to draw samples from unnormalized target distributions. Due to Its scalability and efficiency in high dimensions, the HMC method is widely used in Bayesian inference. However, HMC is typically not efficient when the target distribution is multimodal. I will talk about a novel HMC method that enables efficient sampling from multimodal distributions. This method explores the target space by simulating the Hamiltonian dynamics of a particle with an altered mass. Combined with the recently developed sequential-proposal strategy, this approach can construct Markov chains that make jumps from one density component to another remote component with substantially higher frequency relative to those constructed by standard HMC methods. Search for a remote density component is done in an efficient and robust manner using the geometry of the log target density function. I will demonstrate the favorable numerical efficiency of this new method using a multivariate Gaussian target distribution and an example in a sparse Bayesian regression problem.