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International Journal for Uncertainty Quantification
Impact-faktor: 3.259 5-jähriger Impact-Faktor: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Druckformat: 2152-5080
ISSN Online: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2016018661
pages 501-514

FORWARD AND INVERSE UNCERTAINTY QUANTIFICATION USING MULTILEVEL MONTE CARLO ALGORITHMS FOR AN ELLIPTIC NONLOCAL EQUATION

Ajay Jasra
Department of Statistics & Applied Probability, National University of Singapore, Singapore
Kody J.H. Law
School of Mathematics, University of Manchester, Manchester, M139PL, UK
Yan Zhou
Department of Statistics & Applied Probability National University of Singapore, Singapore

ABSTRAKT

This paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are used for a priori and a posteriori estimation, respectively, of quantities of interest. These algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.