000201609 001__ 201609
000201609 005__ 20190317000005.0
000201609 02470 $$2ISI$$a000354704400004
000201609 0247_ $$a10.1007/s10543-014-0511-3$$2doi
000201609 037__ $$aARTICLE
000201609 245__ $$aA continuation multilevel Monte Carlo algorithm
000201609 260__ $$c2015
000201609 269__ $$a2015
000201609 300__ $$a34
000201609 336__ $$aJournal Articles
000201609 520__ $$aWe propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding variance and weak error. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients.
000201609 6531_ $$aMultilevel Monte Carlo
000201609 6531_ $$aMonte Carlo
000201609 6531_ $$aPartial differential equations with random data
000201609 6531_ $$aStochastic differential equations
000201609 6531_ $$aBayesian inference
000201609 700__ $$aCollier, Nathan
000201609 700__ $$g270909$$aHaji-Ali, Abdul-Lateef$$0250102
000201609 700__ $$g118353$$aNobile, Fabio$$0241873
000201609 700__ $$g226103$$avon Schwerin, Erik$$0246773
000201609 700__ $$aTempone, Raúl
000201609 773__ $$q399-432$$k2$$j55$$tBIT Numerical Mathematics
000201609 787__ $$whttps://infoscience.epfl.ch/record/263220$$eIs New Version Of
000201609 8560_ $$fjulien.junod@epfl.ch
000201609 8564_ $$uhttps://infoscience.epfl.ch/record/201609/files/2015_Collier_HajiAli_Nobile_eal_BIT_Continuation.pdf$$zPublisher's version$$s1856912$$yPublisher's version
000201609 909C0 $$xU12495$$0252411$$pCSQI
000201609 909CO $$qGLOBAL_SET$$pSB$$ooai:infoscience.tind.io:201609$$particle
000201609 917Z8 $$x178574
000201609 917Z8 $$x118353
000201609 917Z8 $$x118353
000201609 937__ $$aEPFL-ARTICLE-201609
000201609 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000201609 980__ $$aARTICLE