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We study Hamiltonian Monte Carlo (HMC) for sampling from a strongly logconcave density proportional to $e^{-f}$ where $f:\mathbb{R}^d \to \mathbb{R}$ is $\mu$-strongly convex and $L$-smooth (the condition number is $\kappa = L/\mu$). We…

Data Structures and Algorithms · Computer Science 2019-05-08 Zongchen Chen , Santosh S. Vempala

Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in complex probabilistic models of continuous variables. In common with many MCMC methods, however, the standard HMC…

Computation · Statistics 2017-04-12 Matthew M. Graham , Amos J. Storkey

Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk behavior typical of many Markov Chain Monte Carlo samplers.…

Hamiltonian Monte Carlo is a popular sampling technique for smooth target densities. The scale lengths of the target have long been known to influence integration error and sampling efficiency. However, quantitative measures intrinsic to…

Computation · Statistics 2020-02-06 Ian Langmore , Michael Dikovsky , Scott Geraedts , Peter Norgaard , Rob Von Behren

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

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible…

Computation · Statistics 2019-07-26 Tijana Radivojević , Elena Akhmatskaya

We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…

Numerical Analysis · Mathematics 2025-02-13 Geoffrey McGregor , Andy T. S. Wan

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…

Computation · Statistics 2019-05-03 Khue-Dung Dang , Matias Quiroz , Robert Kohn , Minh-Ngoc Tran , Mattias Villani

Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain…

Computation · Statistics 2020-06-22 Jonghyun Yun , Minsuk Shin , Ick Hoon Jin , Faming Liang

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

Computation · Statistics 2017-04-19 Cheng Zhang , Babak Shahbaba , Hongkai Zhao

The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…

Computation · Statistics 2025-01-27 Abraham Granados , Isaías Bañales

We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…

Data Analysis, Statistics and Probability · Physics 2016-04-26 Nirag Kadakia

Markov Chain Monte Carlo (MCMC) sampling methods are widely used but often encounter either slow convergence or biased sampling when applied to multimodal high dimensional distributions. In this paper, we present a general framework of…

Computation · Statistics 2017-09-12 Ricky Fok , Aijun An , Xiaogang Wang

We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to…

Data Structures and Algorithms · Computer Science 2021-10-28 Yin Tat Lee , Ruoqi Shen , Kevin Tian

Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth distributions and has motivated the widely used No-U-turn Sampler (NUTS) and software Stan. We build on NUTS and the technique of "unbiased sampling" to design HMC…

Computation · Statistics 2022-12-26 George M. Leigh , Amanda R. Northrop

Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented…

Computation · Statistics 2026-02-09 Julien Stoehr , Alan Benson , Nial Friel

Recently, it has been shown that the hybrid Monte Carlo (HMC) algorithm is guaranteed to converge exponentially to a given target probability distribution $p(x)\propto e^{-V(x)}$ on non-compact spaces if augmented by an appropriate radial…

Computational Physics · Physics 2025-04-28 Johann Ostmeyer

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

Methodology · Statistics 2014-05-13 Tianqi Chen , Emily B. Fox , Carlos Guestrin

Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality, which is typically challenging to resolve in a satisfactory…

Probability · Mathematics 2017-09-08 Nawaf Bou-Rabee , Jesus Maria Sanz-Serna