Results 11 to 20 of about 40,789 (244)
Multilevel Monte Carlo for Reliability Theory
Reliability Engineering & System Safety, 2017 As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a simulation approach which is typically used for stochastic differential equation models - can be applied in reliability ...
Aslett, L. J. M. +2 more
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Unbiased Estimators and Multilevel Monte Carlo [PDF]
Operations Research, 2018 Multilevel Monte Carlo (MLMC) and recently proposed unbiased estimators are closely related. This connection is elaborated by presenting a new general class of unbiased estimators, which admits previous debiasing schemes as special cases. New lower variance estimators are proposed, which are stratified versions of earlier unbiased schemes.
Matti Vihola
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Multilevel Monte Carlo Metamodeling [PDF]
Operations Research, 2013 Approximating the function that maps the input parameters of the simulation model to the expectation of the simulation output is an important and challenging problem in stochastic simulation metamodeling. Because an expectation is an integral, this function approximation problem can be seen as parametric integration—approximating the function that ...
Imry Rosenbaum, Jeremy Staum
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Multilevel sequential Monte Carlo samplers [PDF]
Stochastic Processes and their Applications, 2017 In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a ...
Beskos, Alexandros +4 more
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Multilevel Markov Chain Monte Carlo [PDF]
SIAM Review, 2019 The authors are interested in uncertainty quantification in porous media flow with high-dimensional parameter spaces. This problem is often solved by Markov chain Monte Carlo methods, which have a prohibitively large computational cost. First, the authors propose a new multilevel Metropolis-Hastings algorithm and establish a complexity theorem that ...
Dodwell, T +3 more
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Adaptive Multilevel Monte Carlo for Probabilities
SIAM Journal on Numerical Analysis, 2022 We consider the numerical approximation of $\mathbb{P}[G\in ]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$ which can be sampled.
Abdul-Lateef Haji-Ali +2 more
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Weak Error for Nested Multilevel Monte Carlo [PDF]
Methodology and Computing in Applied Probability, 2020 This article discusses MLMC estimators with and without weights, applied to nested expectations of the form E [f (E [F (Y, Z)|Y ])]. More precisely, we are interested on the assumptions needed to comply with the MLMC framework, depending on whether the payoff function f is smooth or not.
Giorgi, Daphné +2 more
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Multilevel Monte Carlo for solving POMDPs on-line [PDF]
The International Journal of Robotics Research, 2022 Planning under partial observability is essential for autonomous robots. A principled way to address such planning problems is the Partially Observable Markov Decision Process (POMDP). Although solving POMDPs is computationally intractable, substantial advancements have been achieved in developing approximate POMDP solvers in the past two decades ...
Marcus Hoerger +2 more
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Algorithms, 2020 Civil engineering applications are often characterized by a large uncertainty on the material parameters. Discretization of the underlying equations is typically done by means of the Galerkin Finite Element method. The uncertain material parameter can be
Philippe Blondeel +5 more
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Multilevel Monte Carlo Approximation of Functions [PDF]
SIAM/ASA Journal on Uncertainty Quantification, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Krumscheid, Sebastian, Nobile, Fabio
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