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We present a nonlinear (in the sense of McKean) generalization of Hamiltonian Monte Carlo (HMC) termed nonlinear HMC (nHMC) capable of sampling from nonlinear probability measures of mean-field type. When the underlying confinement…

Probability · Mathematics 2023-09-22 Nawaf Bou-Rabee , Katharina Schuh

Hamiltonian Monte Carlo (HMC) is a popular method in sampling. While there are quite a few works of studying this method on various aspects, an interesting question is how to choose its integration time to achieve acceleration. In this…

Machine Learning · Computer Science 2023-02-16 Jun-Kun Wang , Andre Wibisono

This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…

Probability · Mathematics 2024-05-14 Evan Camrud , Alain Durmus , Pierre Monmarché , Gabriel Stoltz

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 obtain several quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm for a strongly log-concave target distribution $\pi$ on $\mathbb{R}^{d}$, showing that HMC mixes quickly in this setting. One of…

Probability · Mathematics 2017-08-24 Oren Mangoubi , Aaron Smith

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the…

Information Theory · Computer Science 2018-07-31 Zheng Wang , Cong Ling

We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves $\varepsilon$ error (in 2-Wasserstein…

Machine Learning · Statistics 2018-01-30 Xiang Cheng , Niladri S. Chatterji , Peter L. Bartlett , Michael I. Jordan

Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution…

Modern implementations of Hamiltonian Monte Carlo and related MCMC algorithms support sampling of probability functions that embed numerical root-finding algorithms, thereby allowing fitting of statistical models involving analytically…

Computation · Statistics 2025-06-19 Teddy Groves , Nicholas Luke Cowie , Lars Keld Nielsen

In this paper, we propose a discontinuous Hamilton Monte Carlo (DHMC) to sample from dimensional varying distributions, and particularly the grand canonical ensemble. The DHMC was proposed in [Biometrika, 107(2)] for discontinuous potential…

Numerical Analysis · Mathematics 2025-05-16 Lei Li , Xiangxian Luo , Yinchen Luo

This work describes methodologies to successfully implement the Implicit Monte Carlo (IMC) scheme for thermal radiative transfer in reduced-precision floating-point arithmetic. The methods used can be broadly categorized into scaling…

Computational Physics · Physics 2025-10-27 Simon Butson , Mathew Cleveland , Alex Long , Todd Palmer

We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex body. We prove that, starting from a warm start, the walk mixes to a log-concave target…

Machine Learning · Computer Science 2023-03-30 Apostolos Chalkis , Vissarion Fisikopoulos , Marios Papachristou , Elias Tsigaridas

Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompatible with motion generated by non-canonical dynamics. These…

Machine Learning · Statistics 2020-08-20 James A. Brofos , Roy R. Lederman

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.…

Splitting schemes are numerical integrators for Hamiltonian problems that may advantageously replace the St\"ormer-Verlet method within Hamiltonian Monte Carlo (HMC) methodology. However, HMC performance is very sensitive to the step size…

Numerical Analysis · Mathematics 2022-12-02 F. Diele , C. Marangi , C. Tamborrino , C. Tarantino

Hamiltonian Monte Carlo (HMC) and related algorithms have become routinely used in Bayesian computation. In this article, we present a simple and provably accurate method to improve the efficiency of HMC and related algorithms with…

Computation · Statistics 2020-03-10 Akihiko Nishimura , David Dunson

Piecewise-deterministic Markov process (PDMP) samplers constitute a state-of-the-art Markov chain Monte Carlo paradigm in Bayesian computation, with examples including the zig-zag and bouncy particle sampler (bps). Recent work on the…

Computation · Statistics 2026-03-10 Andrew Chin , Akihiko Nishimura

We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution,…

Methodology · Statistics 2022-07-20 Chul Moon , Adel Bedoui

Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we use the underlying geometry of Hamiltonian Monte Carlo to…

Methodology · Statistics 2015-02-03 M. J. Betancourt , Simon Byrne , Mark Girolami

Hierarchical Bayesian models based on Gaussian processes are considered useful for describing complex nonlinear statistical dependencies among variables in real-world data. However, effective Monte Carlo algorithms for inference with these…

Machine Learning · Statistics 2025-11-11 Takashi Hayakawa , Satoshi Asai