Optimal Sampling Strategies for Multiscale Stochastic Processes

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dc.citation.bibtexNamearticleen_US
dc.citation.journalTitleInstitute of Mathematical Statistics Lecture Notes - Monograph Seriesen_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.accessioned2007-10-31T01:00:52Zen_US
dc.date.available2007-10-31T01:00:52Zen_US
dc.date.issued2006-01-15en_US
dc.date.modified2006-03-08en_US
dc.date.submitted2006-02-23en_US
dc.descriptionJournal Paperen_US
dc.description.abstractIn this paper, we determine which non-random sampling of fixed size gives the best linear predictor of the sum of a finite spatial population. We employ different multiscale superpopulation models and use the minimum mean-squared error as our optimality criterion. In a multiscale superpopulation tree models, the leaves represent the units of the population, interior nodes represent partial sums of the population, and the root node represents the total sum of the population. We prove that the optimal sampling pattern varies dramatically with the correlation structure of the tree nodes. While <it> uniform sampling </it> is optimal for trees with "positive correlation progression," it provides the worst possible sampling with "negative correlation progression." As an analysis tool, we introduce and study a class of <it> independent innovations trees </it> that are of interest in their own right. We derive a fast water-filling algorithm to determine the optimal sampling of the leaves to estimate the root of an independent innovations tree.en_US
dc.description.sponsorshipDefense Advanced Research Projects Agencyen_US
dc.description.sponsorshipNational Science Foundationen_US
dc.description.sponsorshipNational Science Foundationen_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>Institute of Mathematical Statistics Lecture Notes - Monograph Series,</i> 2006.en_US
dc.identifier.doihttp://dx.doi.org/10.1214/074921706000000509en_US
dc.identifier.urihttps://hdl.handle.net/1911/20260en_US
dc.language.isoengen_US
dc.subjectmultiscale stochastic processesen_US
dc.subjectfinite populationen_US
dc.subjectspatial dataen_US
dc.subjectnetworksen_US
dc.subjectsamplingen_US
dc.subjectconvexen_US
dc.subjectconcaveen_US
dc.subjectoptimizationen_US
dc.subjecttreesen_US
dc.subjectsensor networksen_US
dc.subject.keywordmultiscale stochastic processesen_US
dc.subject.keywordfinite populationen_US
dc.subject.keywordspatial dataen_US
dc.subject.keywordnetworksen_US
dc.subject.keywordsamplingen_US
dc.subject.keywordconvexen_US
dc.subject.keywordconcaveen_US
dc.subject.keywordoptimizationen_US
dc.subject.keywordtreesen_US
dc.subject.keywordsensor networksen_US
dc.subject.otherSignal Processing for Networkingen_US
dc.titleOptimal Sampling Strategies for Multiscale Stochastic Processesen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
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