Multiscale spectral modelling for nonstationary time series within an ordered multiple-trial experiment

dc.contributor.authorEmbleton, Jonathan
dc.contributor.authorKnight, Marina I.
dc.contributor.authorOmbao, Hernando
dc.contributor.departmentStatistics Program
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.institutionDepartment of Mathematics, University of York
dc.date.accessioned2022-09-29T06:54:20Z
dc.date.available2022-09-29T06:54:20Z
dc.date.issued2022
dc.description.abstractWithin the neurosciences it is natural to observe variability across time in the dynamics of an underlying brain process. Wavelets are essential in analysing brain signals because, even within a single trial, brain signals exhibit nonstationary behaviour. However, neurological signals generated within an experiment may also potentially exhibit evolution across trials (replicates), even for identical stimuli. As neurologists consider localised spectra of brain signals to be most informative, we propose the MULtiple-Trials Locally Stationary Wavelet process (MULT-LSW) that fills the gap in the literature by directly giving a stochastic wavelet representation of the time series of ordered replicates itself. MULT-LSW yields a natural desired time- and trial-localisation of the process dynamics, capturing nonstationary behaviour both within and across trials. While current techniques are restricted by the assumption of uncorrelated replicates, here we account for between-trial correlation. We rigorously develop the associated wavelet spectral estimation framework along with its asymptotic properties. By means of thorough simulation studies, we demonstrate the theoretical estimator properties hold in practice. A real data investigation into the evolutionary dynamics of the hippocampus and nucleus accumbens, during an associative learning experiment, demonstrates the applicability of our proposed methodology as well as the new insights it provides. Our model is general and facilitates wider experimental data analysis than the current literature allows.
dc.description.sponsorshipThe first author was supported by EPSRC EP/N509802/1.
dc.eprint.versionPublisher's Version/PDF
dc.identifier.citationEmbleton, J., Knight, M. I., & Ombao, H. (2022). Multiscale spectral modelling for nonstationary time series within an ordered multiple-trial experiment. The Annals of Applied Statistics, 16(4). https://doi.org/10.1214/22-aoas1614
dc.identifier.doi10.1214/22-aoas1614
dc.identifier.issn1932-6157
dc.identifier.issue4
dc.identifier.journalThe Annals of Applied Statistics
dc.identifier.urihttp://hdl.handle.net/10754/681740
dc.identifier.volume16
dc.publisherInstitute of Mathematical Statistics
dc.relation.urlhttps://projecteuclid.org/journals/annals-of-applied-statistics/volume-16/issue-4/Multiscale-spectral-modelling-for-nonstationary-time-series-within-an-ordered/10.1214/22-AOAS1614.full
dc.titleMultiscale spectral modelling for nonstationary time series within an ordered multiple-trial experiment
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Embleton, Jonathan,equals">Embleton, Jonathan</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Knight, Marina I.,equals">Knight, Marina I.</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0001-7020-8091&spc.sf=dc.date.issued&spc.sd=DESC">Ombao, Hernando</a> <a href="https://orcid.org/0000-0001-7020-8091" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Statistics Program,equals">Statistics Program</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division</a><br><br><h5>Date</h5>2022</span>
display.details.right<span><h5>Abstract</h5>Within the neurosciences it is natural to observe variability across time in the dynamics of an underlying brain process. Wavelets are essential in analysing brain signals because, even within a single trial, brain signals exhibit nonstationary behaviour. However, neurological signals generated within an experiment may also potentially exhibit evolution across trials (replicates), even for identical stimuli. As neurologists consider localised spectra of brain signals to be most informative, we propose the MULtiple-Trials Locally Stationary Wavelet process (MULT-LSW) that fills the gap in the literature by directly giving a stochastic wavelet representation of the time series of ordered replicates itself. MULT-LSW yields a natural desired time- and trial-localisation of the process dynamics, capturing nonstationary behaviour both within and across trials. While current techniques are restricted by the assumption of uncorrelated replicates, here we account for between-trial correlation. We rigorously develop the associated wavelet spectral estimation framework along with its asymptotic properties. By means of thorough simulation studies, we demonstrate the theoretical estimator properties hold in practice. A real data investigation into the evolutionary dynamics of the hippocampus and nucleus accumbens, during an associative learning experiment, demonstrates the applicability of our proposed methodology as well as the new insights it provides. Our model is general and facilitates wider experimental data analysis than the current literature allows.<br><br><h5>Citation</h5>Embleton, J., Knight, M. I., & Ombao, H. (2022). Multiscale spectral modelling for nonstationary time series within an ordered multiple-trial experiment. The Annals of Applied Statistics, 16(4). https://doi.org/10.1214/22-aoas1614<br><br><h5>Acknowledgements</h5>The first author was supported by EPSRC EP/N509802/1.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Institute of Mathematical Statistics,equals">Institute of Mathematical Statistics</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=The Annals of Applied Statistics,equals">The Annals of Applied Statistics</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1214/22-aoas1614">10.1214/22-aoas1614</a><br><br><h5>Additional Links</h5>https://projecteuclid.org/journals/annals-of-applied-statistics/volume-16/issue-4/Multiscale-spectral-modelling-for-nonstationary-time-series-within-an-ordered/10.1214/22-AOAS1614.full</span>
kaust.personOmbao, Hernando
orcid.authorEmbleton, Jonathan
orcid.authorKnight, Marina I.
orcid.authorOmbao, Hernando::0000-0001-7020-8091
orcid.id0000-0001-7020-8091
refterms.dateFOA2022-09-29T06:55:43Z
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