QuasiMonte Carlo Integration over NonCubical Domains
(2017) MASM01 20171Mathematical Statistics
 Abstract
 Monte Carlo (MQ) method is a powerful tool to approximate high dimensional integrals. The disadvantage of ordinary MQ is the slow convergence rate by cause of the essential randomness of this method. Computations of this convergence can lead to pure time consuming. QuasiMonte Carlo (QMC) method yields considerably better results since this method is a deterministic alternative which uses LowDiscrepancy sequences instead of random samples . There are a multiplicity of big open problems in QMCmethods, problems partly arising from applications and partly arising from theory. QMC are developed to integrate over unite cube, where it has much more accuracy than MC for integrands of bounded variation. Integration over more general spaces such... (More)
 Monte Carlo (MQ) method is a powerful tool to approximate high dimensional integrals. The disadvantage of ordinary MQ is the slow convergence rate by cause of the essential randomness of this method. Computations of this convergence can lead to pure time consuming. QuasiMonte Carlo (QMC) method yields considerably better results since this method is a deterministic alternative which uses LowDiscrepancy sequences instead of random samples . There are a multiplicity of big open problems in QMCmethods, problems partly arising from applications and partly arising from theory. QMC are developed to integrate over unite cube, where it has much more accuracy than MC for integrands of bounded variation. Integration over more general spaces such as triangles, disks and Cartesian products of such spaces is more challenging for QMC. Nevertheless in realworld applications various problems are deﬁned over such spaces. The aim of this thesis is to provide a survey of a solution of such problems of numerical integration deﬁned over noncubical spaces. We present QMC and randomised QMC (RQMC) constructions in the triangle with a vanishing discrepancy based on the recent work of Basu 2016. The QMC construction is a version of the Van der CorputHalton sequences specially made to the unit triangle. The attraction of scrambled net is replication based error estimation for QMC with slightly the same accuracy as QMC, and for smooth enough integrands. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8904179
 author
 Mortazavi, Nilofar
 supervisor

 Magnus Wiktorsson ^{LU}
 organization
 course
 MASM01 20171
 year
 2017
 type
 H2  Master's Degree (Two Years)
 subject
 language
 English
 id
 8904179
 date added to LUP
 20170306 13:45:11
 date last changed
 20170807 16:59:04
@misc{8904179, abstract = {Monte Carlo (MQ) method is a powerful tool to approximate high dimensional integrals. The disadvantage of ordinary MQ is the slow convergence rate by cause of the essential randomness of this method. Computations of this convergence can lead to pure time consuming. QuasiMonte Carlo (QMC) method yields considerably better results since this method is a deterministic alternative which uses LowDiscrepancy sequences instead of random samples . There are a multiplicity of big open problems in QMCmethods, problems partly arising from applications and partly arising from theory. QMC are developed to integrate over unite cube, where it has much more accuracy than MC for integrands of bounded variation. Integration over more general spaces such as triangles, disks and Cartesian products of such spaces is more challenging for QMC. Nevertheless in realworld applications various problems are deﬁned over such spaces. The aim of this thesis is to provide a survey of a solution of such problems of numerical integration deﬁned over noncubical spaces. We present QMC and randomised QMC (RQMC) constructions in the triangle with a vanishing discrepancy based on the recent work of Basu 2016. The QMC construction is a version of the Van der CorputHalton sequences specially made to the unit triangle. The attraction of scrambled net is replication based error estimation for QMC with slightly the same accuracy as QMC, and for smooth enough integrands.}, author = {Mortazavi, Nilofar}, language = {eng}, note = {Student Paper}, title = {QuasiMonte Carlo Integration over NonCubical Domains}, year = {2017}, }