TY - JOUR

T1 - Forward and inverse uncertainty quantification using multilevel monte carlo algorithms for an elliptic nonlocal equation

AU - Jasra, Ajay

AU - Law, Kody J.H.

AU - Zhou, Yan

N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.dl.begellhouse.com/journals/52034eb04b657aea,3bc93f646a4f7eac,779790a25a0baf83.html

UR - http://www.scopus.com/inward/record.url?scp=85010400019&partnerID=8YFLogxK

U2 - 10.1615/Int.J.UncertaintyQuantification.2016018661

DO - 10.1615/Int.J.UncertaintyQuantification.2016018661

M3 - Article

SN - 2152-5099

VL - 6

JO - International Journal for Uncertainty Quantification

JF - International Journal for Uncertainty Quantification

IS - 6

ER -