Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions

DOI10.1007/s40072-020-00175-6zbMath1470.60202arXiv1909.07962OpenAlexW3101147110MaRDI QIDQ2045410

Nawaf Bou-Rabee, Andreas Eberle

Publication date: 12 August 2021

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.07962

zbMATH Keywords

Hilbert spacesgeometric integrationconvergence to equilibriumhybrid Monte CarlocouplingMetropolis-HastingsHamiltonian Monte CarloMarkov chain Monte Carlo in infinite dimensions

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Monte Carlo methods (65C05) Discrete-time Markov processes on general state spaces (60J05) Numerical analysis or methods applied to Markov chains (65C40) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

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Couplings for Andersen dynamics, On Irreversible Metropolis Sampling Related to Langevin Dynamics, Geometric Ergodicity for Hamiltonian Monte Carlo on Compact Manifolds, Ergodicity and long-time behavior of the Random Batch Method for interacting particle systems, On the accept-reject mechanism for Metropolis-Hastings algorithms, Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models, Geometric numerical integration. Abstracts from the workshop held March 28 -- April 3, 2021 (hybrid meeting), Mixing time guarantees for unadjusted Hamiltonian Monte Carlo

Cites Work

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• Equi-energy sampler with applications in statistical inference and statistical mechanics
• Spectral gaps for a Metropolis-Hastings algorithm in infinite dimensions
• Curvature, concentration and error estimates for Markov chain Monte Carlo
• Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
• Hybrid Monte Carlo on Hilbert spaces
• A note on Metropolis-Hastings kernels for general state spaces
• Ergodicity of dissipative differential equations subject to random impulses
• Randomized Hamiltonian Monte Carlo
• Explicit contraction rates for a class of degenerate and infinite-dimensional diffusions
• Statistical and computational inverse problems.
• Invariant measures of stochastic partial differential equations and conditioned diffusions
• Exponential mixing properties of stochastic PDEs through asymptotic coupling
• Irreducibility and geometric ergodicity of Hamiltonian Monte Carlo
• On the geometric ergodicity of Hamiltonian Monte Carlo
• Couplings and quantitative contraction rates for Langevin dynamics
• Molecular dynamics. With deterministic and stochastic numerical methods
• Optimal tuning of the hybrid Monte Carlo algorithm
• Error bounds for Metropolis-Hastings algorithms applied to perturbations of Gaussian measures in high dimensions
• Subgeometric rates of convergence of Markov processes in the Wasserstein metric
• Monte Carlo strategies in scientific computing.
• Analysis of SPDEs arising in path sampling. II: The nonlinear case
• Analysis of SPDEs arising in path sampling. I: The Gaussian case
• Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations
• Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• Coupling and convergence for Hamiltonian Monte Carlo
• Inverse problems: A Bayesian perspective
• MCMC METHODS FOR DIFFUSION BRIDGES
• Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models
• Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes
• A Bayesian Approach to Estimating Background Flows from a Passive Scalar
• Geometric integrators and the Hamiltonian Monte Carlo method
• The Andersen thermostat in molecular dynamics
• Theoretical and numerical comparison of some sampling methods for molecular dynamics