Reliable error estimation for Sobol' indices

International audienceIn the field of sensitivity analysis, Sobol’ indices are sensitivity measures widely used to assess the importance of inputs of a model to its output. The estimation of these indices is often performed trough Monte Carlo or quasi-Monte Carlo methods. A notable method is the replication procedure that estimates first-order indices at a reduced cost in terms of number of model evaluations. An inherent practical problem of this estimation is how to quantify the number of model evaluations needed to ensure that estimates satisfy a desired error tolerance. This paper addresses this challenge by proposing a reliable error bound for first-order and total effect Sobol’ indices. Starting from the integral formula of the indices, the error bound is defined in terms of the discrete Walsh coefficients of the different integrands.We propose a sequential estimation procedure of Sobol’ indices using the error bound as a stopping criterion. The sequential procedure combines Sobol’ sequences with either Saltelli’s strategy to estimate both first-order and total effect indices, or the replication procedure to estimate only first-order indices

Applications of Guaranteed Adaptive Quasi-Monte Carlo Algorithms

In recent years we have developed adaptive quasi-Monte Carlo (qMC) cubature algorithms using Sobol sequences and integration lattice sequences that meet the error tolerance prescribed by the user. These algorithms have been implemented in MATLAB http://gailgithub.github.io/GAIL_Dev/ and they are guaranteed for integrands whose Fourier series coeffcients decay not too erratically. This talk presents several applications of these adaptive qMC algorithms, including option pricing, multivariate normal probability, and Sobol indices. These examples illustrate how our algorithms need little a priori information. One does not need to know the decay rates of the Fourier coeffcients nor the weights defining the underlying function spaces containing the integrands. We also discuss how these adaptive qMC algorithms can work with other effciency enhancing methods such as control variates and importance sampling. (Joint work with F. J. Hickernell and Da Li.)Non UBCUnreviewedAuthor affiliation: Illinois Institute of TechnologyGraduat