An energy-stepping Markov Monte Carlo method

We introduce the energy-stepping Monte Carlo (ESMC) method, a Markov chain Monte Carlo (MCMC) algorithm based on the conventional dynamical interpretation of the proposal stage but employing an energy-stepping integrator. The energy-stepping integrator is quasi-explicit, symplectic, energy-conservin...

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Detalhes bibliográficos
Autores: Ignacio Romero, Michael Ortiz
Formato: artículo
Fecha de publicación:2025
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/438782
Acesso em linha:https://hdl.handle.net/2117/438782
https://dx.doi.org/10.1007/s11012-025-01997-1
Access Level:acceso abierto
Palavra-chave:Hamiltonian Monte Carlo
Markov chain Monte Carlo
Geometric integration
Energystepping integrator
Àrees temàtiques de la UPC::Energies::Gestió de l'energia
Descrição
Resumo:We introduce the energy-stepping Monte Carlo (ESMC) method, a Markov chain Monte Carlo (MCMC) algorithm based on the conventional dynamical interpretation of the proposal stage but employing an energy-stepping integrator. The energy-stepping integrator is quasi-explicit, symplectic, energy-conserving, and symmetry-preserving. As a result of the exact energy conservation of energy-stepping integrators, ESMC has a 100% acceptance ratio of the proposal states. Numerical tests provide empirical evidence that ESMC affords a number of additional benefits: the Markov chains it generates have weak autocorrelation, it has the ability to explore distant characteristic sets of the sampled probability distribution and it yields smaller errors than chains sampled with Hamiltonian Monte Carlo (HMC) and similar step sizes. Finally, ESMC benefits from the exact symmetry conservation properties of the energy-stepping integrator when sampling from potentials with built-in symmetries, whether explicitly known or not.