skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A geometric approach for computing tolerance bounds for elastic functional data

Journal Article · · Journal of Applied Statistics
ORCiD logo [1];  [1];  [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. The Ohio State Univ., Columbus, OH (United States)
+ Show Author Affiliations

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.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); National Technical Nuclear Forensics Center (NTNFC)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1559543
Report Number(s):
SAND-2018-0108J; 659761; TRN: US2000363
Journal Information:
Journal of Applied Statistics, Vol. 47, Issue 3; ISSN 0266-4763
Publisher:
Taylor & FrancisCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

References (39)

Tolerance bands for functional data: Tolerance Bands for Functional Data journal November 2015
Functional Data Analysis book January 2005
Generative models for functional data using phase and amplitude separation journal May 2013
Recent Developments in Bootstrap Methodology journal May 2003
Shape Analysis of Elastic Curves in Euclidean Spaces journal July 2011
Principal Nested Spheres for Time-Warped Functional Data Analysis journal January 2017
Using Curve-Registration Information for Profile Monitoring journal April 2016
A Geometric Approach to Visualization of Variability in Functional Data journal July 2016
A Geometric Approach to Visualization of Variability in Functional Data text January 2016
Bootstrap Methods and their Application book January 1997
Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models journal October 2018
Bayesian Registration of Functions With a Gaussian Process Prior text January 2017
A geometric approach to pairwise Bayesian alignment of functional data using importance sampling journal January 2017
Looking for Shapes in Two-Dimensional Cluttered Point Clouds journal September 2009
Functional Data Analysis of Amplitude and Phase Variation text January 2015
A Geometric Approach to Visualization of Variability in Functional Data text January 2016
Multispecies for multifunctions: combining four complementary species enhances multifunctionality of sown grassland journal February 2021
Bayesian Registration of Functions With a Gaussian Process Prior journal October 2017
Functional and Shape Data Analysis journal October 2017
Functional Data Analysis of Amplitude and Phase Variation journal November 2015
Generative Models for Functional Data using Phase and Amplitude Separation text January 2012
A Geometric Variational Approach to Bayesian Inference journal April 2019
Improved Tolerance Factors for Multivariate Normal Distributions journal July 2006
Functional Data Analysis book January 2005
Functional Boxplots journal January 2011
Phase 2b Weld Residual Stress Round Robin: Mockup Design and Comparisons of Measurement and Simulation Results conference November 2015
Bayesian sensitivity analysis with the Fisher–Rao metric journal July 2015
Precise matching of PL curves in $\mathbb{R}^N$ in the square root velocity framework journal January 2015
Methods for Characterizing and Comparing Populations of Shock Wave Curves journal November 2013
Segmentation, alignment and statistical analysis of biosignals with application to disease classification journal June 2013
PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals journal June 2000
Combining Registration and Fitting for Functional Models journal September 2008
Laser surface-contouring and spline data-smoothing for residual stress measurement journal April 2004
Automated seizure diagnosis system based on feature extraction and channel selection using EEG signals journal February 2021
Principal Nested Spheres for Time-Warped Functional Data Analysis text January 2017
A New Procedure to Measure Near Yield Residual Stresses Using the Deep Hole Drilling Technique journal August 2008
Methods for Uncertainty Quantification and Comparison of Weld Residual Stress Measurements and Predictions conference October 2017
Rate-Invariant Recognition of Humans and Their Activities journal June 2009
A Geometric Approach to Pairwise Bayesian Alignment of Functional Data Using Importance Sampling preprint January 2015

Figures / Tables (21)

Figure 1(p. 3)figure Figure 1
Figure 2(p. 6)figure Figure 2
Figure 3(p. 12)figure Figure 3
Figure 4(p. 12)figure Figure 4
Figure 5(p. 13)figure Figure 5
Figure 6(p. 14)figure Figure 6
Figure 7(p. 14)figure Figure 7
Table 1(p. 15)table Table 1
Figure 8(p. 16)figure Figure 8
Table 2(p. 16)table Table 2
Figure 9(p. 17)figure Figure 9
Table 3(p. 17)table Table 3
Figure 10(p. 18)figure Figure 10
Figure 11(p. 18)figure Figure 11
Figure 12(p. 18)figure Figure 12
Figure 13(p. 19)figure Figure 13
Figure 14(p. 20)figure Figure 14
Figure 15(p. 20)figure Figure 15
Figure 16(p. 21)figure Figure 16
Figure 17(p. 21)figure Figure 17
Figure 18(p. 22)figure Figure 18

Similar Records

THE MEGAMASER COSMOLOGY PROJECT. VIII. A GEOMETRIC DISTANCE TO NGC 5765b
Journal Article · Mon Feb 01 00:00:00 EST 2016 · Astrophysical Journal · OSTI ID:1559543
+7 more
Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics
Journal Article · Mon Aug 08 00:00:00 EDT 2022 · Chaos: An Interdisciplinary Journal of Nonlinear Science · OSTI ID:1559543
+1 more
Managing discovery risks--A Tevatron case study
Conference · Wed Jul 28 00:00:00 EDT 2004 · OSTI ID:1559543

Related Subjects

97 MATHEMATICS AND COMPUTING
compositional noise
functional data analysis
functional tolerance bounds
functional Principal Component Analysis