Fixed-Distance Hamiltonian Monte Carlo

Hadi Mohasel Afshar, Sally Cripps

Keywords: Markov Chain Monte Carlo, Sampling, Hamiltonian Monte Carlo, Reversible Jump, RJMCMC, No-U-Turn sampler

TL;DR: We propose a variation of HMC where the traversed distance (rather than time) of the simulated dynamics is fixed.

Abstract: We propose a variation of the Hamiltonian Monte Carlo sampling (HMC) where the equations of motion are simulated for a fixed traversed distance rather than the conventional fixed simulation time. This new mechanism tends to generate proposals that have higher target probability values. The momentum distribution that is naturally joint with our Fixed-Distance HMC (FDHMC), and keeps the proposal acceptance probability close to 1, is not Gaussian and generates momentums that have a higher expected magnitude. This translates into a reduced correlation between the successive MCMC states and according to our experimental results, leads to an improvement in terms of the effective sample size per gradient when compared to the baseline HMC and No-U-Turn (NUTS) samplers.