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There is substantial empirical evidence about the success of dynamic implementations of Hamiltonian Monte Carlo (HMC), such as the No U-Turn Sampler (NUTS), in many challenging inference problems but theoretical results about their behavior…

Computation · Statistics 2024-10-21 Alain Durmus , Samuel Gruffaz , Miika Kailas , Eero Saksman , Matti Vihola

In this work we present a new and efficient Bayesian method for nonlinear three dimensional large scale structure inference. We employ a Hamiltonian Monte Carlo (HMC) sampler to obtain samples from a multivariate highly non-Gaussian…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-14 J. Jasche , F. S. Kitaura

In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold. We then combine the notion…

Probability · Mathematics 2015-05-21 Susan Holmes , Simon Rubinstein-Salzedo , Christof Seiler

The pseudofermion action of the Hybrid Monte Carlo (HMC) algorithm for dynamical fermions is modified to directly incorporate Incomplete LU (ILU) factorisation. This reduces the stochastic noise and allows a larger molecular dynamics…

High Energy Physics - Lattice · Physics 2007-05-23 Mike Peardon

We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are…

Machine Learning · Computer Science 2017-11-08 Anirban Roychowdhury , Srinivasan Parthasarathy

Hamiltonian Monte Carlo (HMC) is a very popular and generic collection of Markov chain Monte Carlo (MCMC) algorithms. One explanation for the popularity of HMC algorithms is their excellent performance as the dimension $d$ of the target…

Probability · Mathematics 2018-09-05 Oren Mangoubi , Natesh S. Pillai , Aaron Smith

Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…

Computation · Statistics 2020-06-09 Akihiko Nishimura , David Dunson , Jianfeng Lu

Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) by looking for correlated deviations in pulse arrival times. Current Bayesian searches use Markov Chain Monte Carlo (MCMC) methods, which struggle to sample the…

Instrumentation and Methods for Astrophysics · Physics 2023-03-08 Gabriel E. Freedman , Aaron D. Johnson , Rutger van Haasteren , Sarah J. Vigeland

Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…

Computation · Statistics 2020-05-19 Zexi Song , Zhiqiang Tan

Latent variable models are increasingly used in economics for high-dimensional categorical data like text and surveys. We demonstrate the effectiveness of Hamiltonian Monte Carlo (HMC) with parallelized automatic differentiation for…

Econometrics · Economics 2024-03-04 Szymon Sacher , Laura Battaglia , Stephen Hansen

Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…

Computation · Statistics 2025-04-28 Jimmy Huy Tran , Tore Selland Kleppe

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

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art…

Computational Engineering, Finance, and Science · Computer Science 2024-05-09 Dhruv V. Patel , Jonghyun Lee , Matthew W. Farthing , Peter K. Kitanidis , Eric F. Darve

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…

Computation · Statistics 2021-06-30 Radford M. Neal

We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization…

Machine Learning · Statistics 2019-01-24 Viktor Yanush , Dmitry Kropotov

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Computation · Statistics 2016-10-24 Richard A. Norton , J. Andres Christen , Colin Fox

This paper discusses the irreducibility and geometric ergodicity of the Hamiltonian Monte Carlo (HMC) algorithm. We consider cases where the number of steps of the symplectic integrator is either fixed or random. Under mild conditions on…

Computation · Statistics 2019-05-14 Alain Durmus , Eric Moulines , Eero Saksman

Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as a computationally fast and easily implemented method for performing full Bayesian analysis in hierarchical statistical models. The method relies on introducing a modified…

Computation · Statistics 2018-10-23 Tore Selland Kleppe

Hamiltonian Monte Carlo (HMC) is arguably the dominant statistical inference algorithm used in most popular "first-order differentiable" Probabilistic Programming Languages (PPLs). However, the fact that HMC uses derivative information…

Computation · Statistics 2019-05-31 Bradley Gram-Hansen , Yuan Zhou , Tobias Kohn , Tom Rainforth , Hongseok Yang , Frank Wood

Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential…

Numerical Analysis · Mathematics 2013-12-12 Dmitry Shcherbakov , Matthias Ehrhardt , Michael Günther , Michael Peardon