A0249
Title: Sampling from high-dimensional, multimodal Bayesian posterior using adaptively-tuned, tempered Hamiltonian Monte Carlo
Authors: Joonha Park - University of Kansas (United States) [presenting]
Abstract: Hamiltonian Monte Carlo (HMC) is widely used for sampling high-dimensional target distributions arising from Bayesian posterior. Although HMC scales favorably with increasing dimensions, it is very inefficient when the target distribution is strongly multimodal. Sampling highly multimodal target distributions is often tackled using tempering strategies, but the resulting algorithms are often difficult to tune in practice, especially in high dimensions. A method that combines the tempering strategy with Hamiltonian Monte Carlo is developed in a way that allows efficient sampling of high-dimensional, strongly multimodal distributions. The method consists in proposing a candidate for the next state of the Markov chain by solving the Hamiltonian equations of motion with time-varying mass. Compared to the simulated tempering method or the parallel tempering method, the method has a distinctive advantage in the case where target distribution changes at each iteration, such as in the Gibbs sampler. A careful tuning strategy is developed for the method and an adaptively-tuned, tempered Hamiltonian Monte Carlo (ATHMC) algorithm is proposed. The excellent sampling efficiency of ATHMC is demonstrated for high-dimensional, multimodal distributions using a mixture of Gaussians and a Bayesian posterior distribution for a sensor network self-localization problem.
