Optimal Sampling Strategies for Multiscale Stochastic Processes

dc.citation.bibtexNamearticleen_US
dc.citation.journalTitleErich L. Lehmann Symposiumen_US
dc.contributor.authorRibeiro, Vinay Josephen_US
dc.contributor.authorRiedi, Rudolf H.en_US
dc.contributor.authorBaraniuk, Richard G.en_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T01:00:35Zen_US
dc.date.available2007-10-31T01:00:35Zen_US
dc.date.issued2004-12-01en_US
dc.date.modified2006-07-05en_US
dc.date.submitted2004-12-13en_US
dc.descriptionJournal Paperen_US
dc.description.abstractThis paper studies multiscale stochastic processes which are random processes organized on the nodes of a tree. The random variables at different levels on the tree represent time series of samples of a stochastic process at different temporal or spatial cales. We focus on classes of multiscale processes with additional statistical structure connecting scales and seek an optimal linear estimator of coarse scale nodes using an incomplete set of nodes at a finer time scale. We prove that the optimal solution for any tree with so-called independent innovations is readily given by a polynomial-time algorithm which we term the water-filling algorithm. The optimal solutions vary dramatically with the correlation structure of the multiscale process. For so-called scale-invariant trees and processes with positive correlation progression through scales, uniformly spaced leaves are optimal and clustered leaves are the worst possible. For processes with negative correlation progression, uniformly spaced leaves are the worst possible. Our results have implications for network traffic estimation, sensor network design, and environmental monitoring.en_US
dc.description.sponsorshipTexas Instrumentsen_US
dc.description.sponsorshipDefense Advanced Research Projects Agencyen_US
dc.description.sponsorshipNational Science Foundationen_US
dc.identifier.citationV. J. Ribeiro, R. H. Riedi and R. G. Baraniuk, "Optimal Sampling Strategies for Multiscale Stochastic Processes," <i>Erich L. Lehmann Symposium,</i> 2004.en_US
dc.identifier.urihttps://hdl.handle.net/1911/20254en_US
dc.language.isoengen_US
dc.relation.projecthttp://www.dsp.rice.eduen_US
dc.relation.softwarehttp://www.dsp.rice.eduen_US
dc.relation.urihttp://www.jstor.org/stable/4356403en_US
dc.subjectmultiscale stochastic processesen_US
dc.subjectnetworksen_US
dc.subjectlong-range-dependenceen_US
dc.subjectsamplingen_US
dc.subjectoptimalen_US
dc.subjecttreesen_US
dc.subjectsensor networksen_US
dc.subject.keywordmultiscale stochastic processesen_US
dc.subject.keywordnetworksen_US
dc.subject.keywordlong-range-dependenceen_US
dc.subject.keywordsamplingen_US
dc.subject.keywordoptimalen_US
dc.subject.keywordtreesen_US
dc.subject.keywordsensor networksen_US
dc.subject.otherMultiscale Methodsen_US
dc.titleOptimal Sampling Strategies for Multiscale Stochastic Processesen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
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