Light PhD Seminar: Numerical integration in Hamiltonian Monte Carlo

Location: Maryam Mirzakhani Seminar Room at BCAM

Title
Numerical integration in Hamiltonian Monte Carlo

Abstract
Hamiltonian Monte Carlo (HMC) has been widely recognized as a powerful tool for sampling in molecular simulation and Bayesian Statistics. HMC combines a deterministic proposal - using Hamiltonian dynamics - with stochastic Monte Carlo in order to generate correlated samples from a target distribution. The accuracy of numerical integration of the Hamiltonian equations of motions affects the acceptance rate of Monte Carlo trials, and thus is crucial for performance of HMC. In this talk, after giving a brief overview on multi-stage splitting integration schemes used in the HMC context, we present a novel Adaptive Integration Approach (we call it s-AIA) that detects the optimal multi-stage integrator in terms of the best conservation of energy for harmonic forces, being able to achieve a competitive sampling efficiency in HMC Bayesian inference applications.