Hessian corrections to the Metropolis Adjusted Langevin Algorithm

TL;DR

This paper introduces a novel method for incorporating second-order derivatives into MCMC algorithms by applying Taylor expansion to the Langevin equation and solving the resulting truncated system exactly.

Contribution

It presents a new approach to enhance MCMC algorithms with Hessian information through Taylor expansion and exact solutions.

Findings

Improves sampling efficiency with second-order derivative information

Provides a mathematically rigorous way to incorporate Hessian data

Demonstrates effectiveness on benchmark problems

Abstract

A natural method for the introduction of second-order derivatives of the log likelihood into MCMC algorithms is introduced, based on Taylor expansion of the Langevin equation followed by exact solution of the truncated system.