Adaptive variational Hamiltonian Monte Carlo sampling with application to ocean acoustics

Abstract

The Hamiltonian Monte Carlo (HMC) algorithm is a variant Markov Chain Monte Carlo (MCMC) excelling at sampling high dimensional target distributions. The HMC explores a distribution as a particle trajectory in a Hamiltonian system by augmenting distribution parameters with auxiliary momentum variables. A particle trajectory is numerically integrated from initial point to some distant low-correlation point. Projecting back to parameter space yields a proposal point with high acceptance probability leading to faster exploration of the target distribution. The Leap-frog integrator is commonly used for its volume preservation (symplecticity) and reversibility traits that maintain the detailed balance condition of MCMC. Although effective, Leap-frog has sensitivity to choice of integration step-size and number of integration steps. Poor choices cause slow exploration or bias when regions of the distribution are not explored. Adaptive step methods could remove step size issues and explore regions of a distribution where Leap-frog fails. Existing adaptive methods self-adjust step-size while maintaining symplecticity and reversibility. In this work, we apply adaptive step methods to simulated target distributions and real world ocean acoustic data and compare performance. [Work supported by Office of Naval Research.]