Monomial Gamma Monte Carlo Sampling

We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling by demonstrating their connection under the canonical transformation from Hamiltonian mechanics. This insight enables us to extend HMC and slice sampling to a broader family of samplers, called monomial Gamma samplers (MGS). We analyze theoretically the mixing performance of such samplers by proving that the MGS draws samples from a target distribution with zero-autocorrelation, in the limit of a single parameter. This property potentially allows us to generating decorrelated samples, which is not achievable by existing MCMC algorithms. We further show that this performance gain is obtained at a cost of increasing the complexity of numerical integrators. Our theoretical results are validated with synthetic data and real-world applications.