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We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…

Computation · Statistics 2013-06-06 Ari Pakman , Liam Paninski

In Hamiltonian Monte Carlo sampling, the shape of the potential and the choice of the momentum distribution jointly give rise to the Hamiltonian dynamics of the sampler. An efficient sampler propagates quickly in all regions of the…

Cosmology and Nongalactic Astrophysics · Physics 2026-01-28 Javier Silva Lafaurie , Lorne Whiteway , Elena Sellentin , Kutay Nazli , Andrew H. Jaffe , Alan F. Heavens , Arthur Loureiro

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method that allows to sample high dimensional probability measures. It relies on the integration of the Hamiltonian dynamics to propose a move which is then accepted or rejected…

Numerical Analysis · Mathematics 2023-08-08 Tony Lelièvre , Régis Santet , Gabriel Stoltz

We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the Hamiltonian $H$ as $H_0(\theta,p)+U_1(\theta)$, where $H_0$ is quadratic and $U_1$ small. We show that, in general, such samplers suffer from stepsize stability…

Computation · Statistics 2022-07-18 Fernando Casas , Jesús María Sanz-Serna , Luke Shaw

The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $\pi(x) \propto e^{-f(x)}$. We focus on the "idealized" case, where one can…

Data Structures and Algorithms · Computer Science 2021-08-30 Nisheeth K. Vishnoi

This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…

Computation · Statistics 2018-04-20 Ziqi Wang , Marco Broccardo , Junho Song

Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often…

Methodology · Statistics 2023-05-23 Konstantinos G. Papakonstantinou , Hamed Nikbakht , Elsayed Eshra

We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by "splitting" the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is…

Computation · Statistics 2012-07-17 Babak Shahbaba , Shiwei Lan , Wesley O. Johnson , Radford M. Neal

Hybrid Monte-Carlo (HMC) sampling smoother is a fully non-Gaussian four-dimensional data assimilation algorithm that works by directly sampling the posterior distribution formulated in the Bayesian framework. The smoother in its original…

Numerical Analysis · Computer Science 2016-12-21 Ahmed Attia , Razvan Stefanescu , Adrian Sandu

Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the…

Statistical Mechanics · Physics 2021-07-20 Akihisa Ichiki , Masayuki Ohzeki

Hamiltonian Monte Carlo (HMC) is the mainstay of applied Bayesian inference for differentiable models. However, HMC still struggles to sample from hierarchical models that induce densities with multiscale geometry: a large step size is…

Computation · Statistics 2026-02-09 Gilad Turok , Chirag Modi , Bob Carpenter

Bayesian formulation of modern day signal processing problems has called for improved Markov chain Monte Carlo (MCMC) sampling algorithms for inference. The need for efficient sampling techniques has become indispensable for high…

Computation · Statistics 2025-10-28 Apratim Shukla , Dootika Vats , Eric C. Chi

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in…

Machine Learning · Statistics 2020-10-20 Difan Zou , Pan Xu , Quanquan Gu

We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…

Machine Learning · Statistics 2024-01-11 Denny Thaler , Somayajulu L. N. Dhulipala , Franz Bamer , Bernd Markert , Michael D. Shields

We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…

Machine Learning · Statistics 2017-09-12 Kexin Yi , Finale Doshi-Velez

Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand,…

Machine Learning · Computer Science 2019-07-03 Diego Vergara , Sergio Hernández , Matias Valdenegro-Toro , Felipe Jorquera

We propose a variant of Hamiltonian Monte Carlo (HMC), called the Repelling-Attracting Hamiltonian Monte Carlo (RAHMC), for sampling from multimodal distributions. The key idea that underpins RAHMC is a departure from the conservative…

Statistics Theory · Mathematics 2024-03-08 Siddharth Vishwanath , Hyungsuk Tak

Generating samples from a continuous probability density is a central algorithmic problem across statistics, engineering, and the sciences. For high-dimensional settings, Hamiltonian Monte Carlo (HMC) is the default algorithm across…

Data Structures and Algorithms · Computer Science 2026-03-25 Matthew S. Zhang , Jason M. Altschuler , Sinho Chewi

Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time…

Machine Learning · Statistics 2016-09-15 Xiaoyu Lu , Valerio Perrone , Leonard Hasenclever , Yee Whye Teh , Sebastian J. Vollmer

Diffusion models (DMs) have recently shown remarkable performance on inverse problems (IPs). Optimization-based methods can fast solve IPs using DMs as powerful regularizers, but they are susceptible to local minima and noise overfitting.…

Machine Learning · Computer Science 2026-04-21 Yingzhi Xia , Setthakorn Tanomkiattikun , Liangli Zhen , Zaiwang Gu