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dc.contributor.authorYang, Jingjing
Zhu, Hongxiao
Choi, Taeryon
Cox, Dennis D.
dc.date.accessioned 2017-05-22T18:57:18Z
dc.date.available 2017-05-22T18:57:18Z
dc.date.issued 2016
dc.identifier.citation Yang, Jingjing, Zhu, Hongxiao, Choi, Taeryon, et al.. "Smoothing and Mean–Covariance Estimation of Functional Data with a Bayesian Hierarchical Model." Bayesian Analysis, 11, no. 3 (2016) Project Euclid: 649-670. http://dx.doi.org/10.1214/15-BA967.
dc.identifier.urihttps://hdl.handle.net/1911/94338
dc.description.abstract Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data analysis, the issue of smoothing all functional observations simultaneously is less studied. Existing methods often focus on smoothing each individual function separately, at the risk of removing important systematic patterns common across functions. We propose a nonparametric Bayesian approach to smooth all functional observations simultaneously and nonparametrically. In the proposed approach, we assume that the functional observations are independent Gaussian processes subject to a common level of measurement errors, enabling the borrowing of strength across all observations. Unlike most Gaussian process regression models that rely on pre-specified structures for the covariance kernel, we adopt a hierarchical framework by assuming a Gaussian process prior for the mean function and an Inverse-Wishart process prior for the covariance function. These prior assumptions induce an automatic mean–covariance estimation in the posterior inference in addition to the simultaneous smoothing of all observations. Such a hierarchical framework is flexible enough to incorporate functional data with different characteristics, including data measured on either common or uncommon grids, and data with either stationary or nonstationary covariance structures. Simulations and real data analysis demonstrate that, in comparison with alternative methods, the proposed Bayesian approach achieves better smoothing accuracy and comparable mean–covariance estimation results. Furthermore, it can successfully retain the systematic patterns in the functional observations that are usually neglected by the existing functional data analyses based on individual-curve smoothing.
dc.language.iso eng
dc.publisher Project Euclid
dc.rights Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.title Smoothing and Mean–Covariance Estimation of Functional Data with a Bayesian Hierarchical Model
dc.type Journal article
dc.citation.journalTitle Bayesian Analysis
dc.subject.keywordfunctional data
smoothing
Bayesian hierarchical model
Gaussian process, Matérn covariance function
empirical Bayes
dc.citation.volumeNumber 11
dc.citation.issueNumber 3
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1214/15-BA967
dc.type.publication publisher version
dc.citation.firstpage 649
dc.citation.lastpage 670


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