# Selecting the Metric in Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/1905.11916 · HTML: https://mlsanity.com/paper/1905.11916/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 3 of 3)

- [Pathfinder: Parallel quasi-Newton variational inference](https://mlsanity.com/paper/2108.03782/) (2021)
- [AutoStep: Locally adaptive involutive MCMC](https://mlsanity.com/paper/2410.18929/) (2024)
- [Stochastic Gradient Variational Inference with Price's Gradient Estimator from Bures-Wasserstein to Parameter Space](https://mlsanity.com/paper/2602.18718/) (2026)

## Abstract (arXiv)

We present a selection criterion for the Euclidean metric adapted during warmup in a Hamiltonian Monte Carlo sampler that makes it possible for a sampler to automatically pick the metric based on the model and the availability of warmup draws. Additionally, we present a new adaptation inspired by the selection criterion that requires significantly fewer warmup draws to be effective. The effectiveness of the selection criterion and adaptation are demonstrated on a number of applied problems. An implementation for the Stan probabilistic programming language is provided.