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Multilevel quasi-Monte Carlo methods for lognormal diffusion problems
In this paper we present a rigorous cost and error analysis of amultilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC)lattice rules for lognormal diffusion problems. These problems are motivatedby uncertainty...
Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems [M. Eigel, M....
math.NA cs.NA math.ST stat.TH 15A23 15A69 65C60 65D32 65D15 41A10 Markov Chain Monte Carlo inverse problems /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics /dk/atira/pure/subjectarea/asjc/2600/2607 name=Discrete Mathematics and Combinatorics /dk/atira/pure/subjectarea/asjc/2600/2613 name=Statistics and Probability /dk/atira/pure/subjectarea/asjc/1800/1804 name=Statistics, Probability and Uncertainty /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation
Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems [M. Eigel, M....
math.NA cs.NA math.ST stat.TH 15A23 15A69 65C60 65D32 65D15 41A10 Markov Chain Monte Carlo inverse problems /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics /dk/atira/pure/subjectarea/asjc/2600/2607 name=Discrete Mathematics and Combinatorics /dk/atira/pure/subjectarea/asjc/2600/2613 name=Statistics and Probability /dk/atira/pure/subjectarea/asjc/1800/1804 name=Statistics, Probability and Uncertainty /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation
Multilevel quasi-Monte Carlo methods for lognormal diffusion problems
In this paper we present a rigorous cost and error analysis of amultilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC)lattice rules for lognormal diffusion problems. These problems are motivatedby uncertainty...