A geometric approach for computing tolerance bounds for elastic functional data
Abstract
We design an approach for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. Our report is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Moreover, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods.
- Authors:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- The Ohio State Univ., Columbus, OH (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); National Technical Nuclear Forensics Center (NTNFC)
- OSTI Identifier:
- 1559543
- Report Number(s):
- SAND-2018-0108J
Journal ID: ISSN 0266-4763; 659761; TRN: US2000363
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Applied Statistics
- Additional Journal Information:
- Journal Volume: 47; Journal Issue: 3; Journal ID: ISSN 0266-4763
- Publisher:
- Taylor & Francis
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; compositional noise; functional data analysis; functional tolerance bounds; functional Principal Component Analysis
Citation Formats
Tucker, J. Derek, Lewis, John R., King, Caleb, and Kurtek, Sebastian. A geometric approach for computing tolerance bounds for elastic functional data. United States: N. p., 2019.
Web. doi:10.1080/02664763.2019.1645818.
Tucker, J. Derek, Lewis, John R., King, Caleb, & Kurtek, Sebastian. A geometric approach for computing tolerance bounds for elastic functional data. United States. https://doi.org/10.1080/02664763.2019.1645818
Tucker, J. Derek, Lewis, John R., King, Caleb, and Kurtek, Sebastian. Tue .
"A geometric approach for computing tolerance bounds for elastic functional data". United States. https://doi.org/10.1080/02664763.2019.1645818. https://www.osti.gov/servlets/purl/1559543.
@article{osti_1559543,
title = {A geometric approach for computing tolerance bounds for elastic functional data},
author = {Tucker, J. Derek and Lewis, John R. and King, Caleb and Kurtek, Sebastian},
abstractNote = {We design an approach for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. Our report is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Moreover, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods.},
doi = {10.1080/02664763.2019.1645818},
journal = {Journal of Applied Statistics},
number = 3,
volume = 47,
place = {United States},
year = {Tue Jul 23 00:00:00 EDT 2019},
month = {Tue Jul 23 00:00:00 EDT 2019}
}
Web of Science
Figures / Tables:
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