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Towards Unifying Hamiltonian Monte Carlo and Slice Sampling

Yizhe Zhang · Xiangyu Wang · Changyou Chen · Ricardo Henao · Kai Fan · Lawrence Carin

Area 5+6+7+8 #5

Keywords: [ (Other) Bayesian Inference ] [ MCMC ] [ (Other) Statistics ]


We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical analysis of the mixing performance of such samplers, proving that in the limit of a single parameter, the MGS draws decorrelated samples from the desired target distribution. We further show that as this parameter tends toward this limit, performance gains are achieved at a cost of increasing numerical difficulty and some practical convergence issues. Our theoretical results are validated with synthetic data and real-world applications.

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