# Hessian corrections to Hybrid Monte Carlo

## TL;DR

This paper introduces a novel approach to Hybrid Monte Carlo that incorporates second-order derivatives of the log likelihood, improving efficiency by computing the Hessian only at trajectory endpoints.

## Contribution

The method allows Hessian information to be used in HMC without the need for frequent Hessian evaluations during trajectories, enhancing computational efficiency.

## Key findings

- Hessian corrections improve sampling accuracy in HMC.
- The method reduces computational cost compared to traditional Hessian-based approaches.
- Hessian evaluations are limited to start and end points of trajectories.

## Abstract

A method for the introduction of second-order derivatives of the log likelihood into HMC algorithms is introduced, which does not require the Hessian to be evaluated at each leapfrog step but only at the start and end of trajectories.