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Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media [PDF]
Royal Society Open Science, 2017 In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during ...
D. Crevillén-García, H. Power
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A Continuation Multilevel Monte Carlo algorithm [PDF]
BIT Numerical Mathematics, 2014 We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error ...
Collier, Nathan +4 more
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A review of efficient Multilevel Monte Carlo algorithms for derivative pricing and risk management [PDF]
MethodsX, 2023 In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithms, in the paradigm of applications in financial engineering.
Devang Sinha, Siddhartha P. Chakrabarty
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Advanced Multilevel Monte Carlo Methods [PDF]
International Statistical Review, 2020 SummaryThis article reviews the application of some advanced Monte Carlo techniques in the context of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations, which can be biassed in some sense, for instance, by using the discretization of an associated probability law.
Ajay Jasra, Kody Law, Carina Suciu
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Adaptive Multilevel Splitting for Monte Carlo particle transport [PDF]
EPJ Web of Conferences, 2017 In the Monte Carlo simulation of particle transport, and especially for shielding applications, variance reduction techniques are widely used to help simulate realisations of rare events and reduce the relative errors on the estimated scores for a given ...
Louvin Henri +4 more
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A Multilevel Monte Carlo Estimator for Matrix Multiplication [PDF]
SIAM Journal on Scientific Computing, 2020 Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data.
Polydorides, Nick, Wu, Yue
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Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems [PDF]
Mathematics of Computation, 2016 In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in
Kuo, Frances Y. +4 more
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From rough path estimates to multilevel Monte Carlo [PDF]
SIAM Journal on Numerical Analysis, 2016 New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential equations ...
Bayer, Christian +3 more
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Bayesian model selection for multilevel models using integrated likelihoods.
PLoS ONE, 2023 Multilevel linear models allow flexible statistical modelling of complex data with different levels of stratification. Identifying the most appropriate model from the large set of possible candidates is a challenging problem. In the Bayesian setting, the
Tom Edinburgh, Ari Ercole, Stephen Eglen
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Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding [PDF]
Natural Hazards and Earth System Sciences, 2022 When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high-fidelity models being more expensive than low-fidelity ones.
M. C. A. Clare +6 more
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