Sunday 6 April from 15:00-16:00.
ANOVA, global sensitivity, Sobol' indices and all that
Keywords: Analysis of variance; Global sensitivity analysis; Sobol' indices; Variable importance
The analysis of variance (ANOVA) originated in Fisher and MacKenzie's exploration of potato yields. It now plays an important role in numerical approximation and quadrature. This tutorial explains the motivation and uses of the ANOVA decomposition. It was generalized by Hoeffding and independently by Sobol' to the $d$ dimensional unit cube, following two different (essentially opposite) approaches. The ANOVA can be used to measure the effective dimension of an integrand. It can also be used, via Sobol' sensitivity indices, to measure the importance of various sets of input variables to a function. Much of the power of Sobol' indices comes from the fact that they can be directly estimated for any specific function of interest to the user. Those estimates are based on some of Sobol's identities that express the sensitivity measures as integrands over $2d$ dimensions.
Sunday 6 April from 16:00-17:00.
An introduction to multilevel Monte Carlo methods
Keywords: Multilevel Monte Carlo
This tutorial will give an introduction to multilevel Monte Carlo methods, first developed by Stefan Heinrich and Mike Giles. There are now over 30 research groups worldwide using the approach for a huge variety of applications, and many of these groups will be giving presentations on their latest research during the main conference.
The emphasis in the tutorial will be on the essential simplicity of the multilevel approach, and its adaptability to different application areas. It can be viewed as a recursive control variate strategy in which simulations are performed at different levels of accuracy, with the coarser simulations being used as a control variate for the finer simulations. This leads to a great reduction in computational cost because relatively few very accurate, but very expensive, simulations are required – most of the simulations are of low accuracy, at a correspondingly low computational cost.
Applications which will be covered include: financial options, stochastic biochemical reaction modelling, stochastic modelling of groundwater flows, and engineering uncertainty quantification.
Further information about MLMC research worldwide, as well as my own, can be found at http://people.maths.ox.ac.uk/gilesm/mlmc_community.html, http://people.maths.ox.ac.uk/gilesm/mlmc.html and http://people.maths.ox.ac.uk/gilesm/slides.html.
The tutorial slides will be available from http://people.maths.ox.ac.uk/gilesm/talks/mcqmc14_tutorial.pdf.