Show simple item record

FieldValueLanguage
dc.contributor.authorSong, Chenxiao
dc.date.accessioned2022-12-14T23:00:08Z
dc.date.available2022-12-14T23:00:08Z
dc.date.issued2022en_AU
dc.identifier.urihttps://hdl.handle.net/2123/29801
dc.description.abstractMonte Carlo variance reduction methods have attracted significant interest due to the continuous demand for reducing computational costs in various fields of application. This thesis is based on the content of a collection of six papers contributing to the theory and application of Monte Carlo methods and variance reduction techniques. For theoretical developments, we establish a novel framework of Monte Carlo integration over simplices, throughout from sampling to variance reduction. We also investigate the effect of batching for adaptive variance reduction, which aims at running the Monte Carlo simulation simultaneously with the parameter search algorithm using a common sequence of random realizations. Such adaptive variance reduction is moreover employed by strata in a newly proposed stratified sampling framework with dynamic budget allocation. For application in estimating the probability of failure in the context of structural reliability analysis, we formulate adaptive frameworks of stratified sampling with variance reduction by strata as well as stratified directional importance sampling, and survey a variety of numerical approaches employing Monte Carlo methods.en_AU
dc.language.isoenen_AU
dc.subjectMonte Carlo methodsen_AU
dc.subjectvariance reductionen_AU
dc.subjectimportance samplingen_AU
dc.subjectstratified samplingen_AU
dc.subjectadaptive simulationen_AU
dc.subjectstructural reliability analysisen_AU
dc.titleMonte Carlo Variance Reduction Methods with Applications in Structural Reliability Analysisen_AU
dc.typeThesis
dc.type.thesisDoctor of Philosophyen_AU
dc.rights.otherThe author retains copyright of this thesis. It may only be used for the purposes of research and study. It must not be used for any other purposes and may not be transmitted or shared with others without prior permission.en_AU
usyd.facultySeS faculties schools::Faculty of Science::School of Mathematics and Statisticsen_AU
usyd.degreeDoctor of Philosophy Ph.D.en_AU
usyd.awardinginstThe University of Sydneyen_AU
usyd.advisorKawai, Reiichiro


Show simple item record

Associated file/s

Associated collections

Show simple item record

There are no previous versions of the item available.