Slice Sampling on Hamiltonian Trajectories

Hamiltonian Monte Carlo and slice sampling are amongst the most widely used and studied classes of Markov Chain Monte Carlo samplers. We connect these two methods and present Hamiltonian slice sampling, which allows slice sampling to be carried out along Hamiltonian trajectories, or transformations thereof. Hamiltonian slice sampling clarifies a class of model priors that induce closed-form slice samplers. More pragmatically, inheriting properties of slice samplers, it offers advantages over Hamiltonian Monte Carlo, in that it has fewer tunable hyperparameters and does not require gradient information. We demonstrate the utility of Hamiltonian slice sampling out of the box on problems ranging from Gaussian process regression to Pitman-Yor based mixture models.