Multilevel Markov Chain Monte Carlo

DOI10.1137/19M126966XzbMath1432.65008OpenAlexW2965797527MaRDI QIDQ5232352

A. L. Teckentrup, Tim Dodwell, Christian Ketelsen, Robert Scheichl

Publication date: 2 September 2019

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m126966x

zbMATH Keywords

finite element analysisMetropolis-Hastings algorithmsmultilevel Monte Carloelliptic PDEs with random coefficientslog-normal coefficients

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Bayesian inference (62F15) Markov processes: estimation; hidden Markov models (62M05) Monte Carlo methods (65C05) Flows in porous media; filtration; seepage (76S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical analysis or methods applied to Markov chains (65C40) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (11)

Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion ⋮ A Micro-Macro Markov Chain Monte Carlo Method for Molecular Dynamics using Reaction Coordinate Proposals ⋮ Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems ⋮ Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes ⋮ A unified performance analysis of likelihood-informed subspace methods ⋮ Full-field order-reduced Gaussian process emulators for nonlinear probabilistic mechanics ⋮ Multi-agent reinforcement learning aided sampling algorithms for a class of multiscale inverse problems ⋮ Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems ⋮ High-performance modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites ⋮ Error Bounds for Some Approximate Posterior Measures in Bayesian Inference ⋮ Improved efficiency of multilevel Monte Carlo for stochastic PDE through strong pairwise coupling

Uses Software

• UMFPACK
• FreeFem++

Cites Work

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