Ensemble preconditioning for Markov chain Monte Carlo simulation. We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighbouring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics, thus providing a practical approach to difficult anisotropic sampling problems in high dimensions. Numerical experiments with model problems demonstrate that dramatic potential speedups, compared to various alternative schemes, are attainable.
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References in zbMATH (referenced in 6 articles , 1 standard article )
Showing results 1 to 6 of 6.
- Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M.: Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler (2020)
- Garbuno-Inigo, Alfredo; Nüsken, Nikolas; Reich, Sebastian: Affine invariant interacting Langevin dynamics for Bayesian inference (2020)
- Heber, Frederik; Trst’anová, Žofia; Leimkuhler, Benedict: Posterior sampling strategies based on discretized stochastic differential equations for machine learning applications (2020)
- Nüsken, N.; Pavliotis, G. A.: Constructing sampling schemes via coupling: Markov semigroups and optimal transport (2019)
- Leimkuhler, Benedict; Matthews, Charles; Weare, Jonathan: Ensemble preconditioning for Markov chain Monte Carlo simulation (2018)
- Duncan, A. B.; Nüsken, N.; Pavliotis, G. A.: Using perturbed underdamped Langevin dynamics to efficiently sample from probability distributions (2017)