Transcription of Tutorial on quasi-Monte Carlo methods
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Tutorial on quasi-Monte Carlo methods
Tutorial onquasi- monte Carlo methodsJosef DickSchool of Mathematics and Statistics, UNSW, Sydney, MCMC, MC, QMCR oughly speaking: Markov chain monte Carlo and quasi - monte Carlo are fordifferent types of problems; If you have a problem where monte Carlo does not work, thenchances are quasi - monte Carlo will not work as well; If monte Carlo works, but you want a faster method try(randomized) quasi - monte Carlo (some tweaking might benecessary). quasi - monte Carlo is an "experimental design" approach toMonte Carlo simulation;In this talk we shall discuss how quasi - monte Carlo can be faster thanMonte Carlo under certain ,REPRODUCING KERNELHILBERTSPACES AND WORST-CASE ERRORQUASI-MONTECARLO POINT SETSRANDOMIZATIONSWEIGHTED FUNCTION SPACES ANDTRACTABILITYThe task is to approximate an integralIs(f) = [0,1]sf(z)dzfor some integrandfby some quadrature ruleQN,s(f) =1NN 1 n=0f(xn)at some sample pointsx0,..,xN 1 [0,1]s. [0,1]sf(x)dx 1NN 1 n=0f(xn)In other words:Area under curve = Volume of cube average function value.
Tutorial on quasi-Monte Carlo methods Josef Dick School of Mathematics and Statistics, UNSW, Sydney, Australia josef.dick@unsw.edu.au
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