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Functional Data

Bayesian Registration of Functions With a Gaussian Process Prior

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Pages 894-904 | Received 01 May 2016, Published online: 13 Oct 2017

References

  • Bhattachayya, A. (1943), “On a Measure of Divergence Between Two Statistical Population Defined by Their Population Distributions,” Bulletin Calcutta Mathematical Society, 35, 99–109.
  • Chau, T. (2001), “A Review of Analytical Techniques for Gait Data. Part 1: Fuzzy, Statistical and Fractal Methods,” Gait & Posture, 13, 49–66.
  • Cheng, W., Dryden, I. L., and Huang, X. (2016), “Bayesian Registration of Functions and Curves,” Bayesian Analysis, 11, 447–475.
  • Claeskens, G., Silverman, B. W., and Slaets, L. (2010), “A Multiresolution Approach to Time Warping Achieved by a Bayesian Prior-Posterior Transfer Fitting Strategy,” Journal of the Royal Statistical Society, 72, 673–694.
  • Clifford, D., Stone, G., Montoliu, I., Rezzi, S., Martin, F.-P., Guy, P., Bruce, S., and Kochhar, S. (2009), “Alignment Using Variable Penalty Dynamic Time Warping,” Analytical Chemistry, 81, 1000–1007.
  • Cotter, S. L., Roberts, G. O., Stuart, A. M., and White, D. (2013), “MCMC Methods for Functions: Modifying Old Algorithms to Make them Faster,” Statistical Science, 28, 424–446.
  • Duhamel, A., Bourriez, J. L., Devos, P., Krystkowiak, P., Destee, A., Derambure, P., and Defebvre, L. (2004), “Statistical Tools for Clinical Gait Analysis,” Gait & Posture, 20, 204–212.
  • Gervini, D., and Gasser, T. (2004), “Self-Modeling Warping Functions,” Journal of the Royal Statistical Society, 66, 959–971.
  • Helwig, N. E., Hong, S., Hsiao-Wecksler, E. T., and Polk, J. D. (2011), “Methods to Temporally Align Gait Cycle Data,” Journal of Biomechanics, 44, 561–566.
  • James, G. (2007), “Curve Alignment by Moments,” Annals of Applied Statistics, 1, 480–501.
  • Kadaba, M. P., Ramakrishnan, H. K., Wootten, M. E., Gainey, J., Gorton, G., and Cochran, G. V. B. (1989), “Repeatability of Kinematic, Kinetic, and Electromyographic Data in Normal Adult Gait,” Journal of Orthopaedic Research, 7, 849–860.
  • Karcher, H. (1977), “Riemannian Center of Mass and Mollifier Smoothing,” Communications on Pure and Applied Mathematics, 30, 509–541.
  • Keogh, E. J., and Pazzani, M. J. (2001), “Derivative Dynamic Time Warping,” in SIAM Proceedings of the International Conference on Data Mining, pp. 1–11.
  • Kneip, A., Li, X., MacGibbon, K. B., and Ramsay, J. O. (2000), “Curve Registration by Local Regression,” The Canadian Journal of Statistics, 28, 19–29.
  • Kneip, A., and Ramsay, J. O. (2008), “Combining Registration and Fitting for Functional Models,” Journal of the American Statistical Association, 103, 1155–1165.
  • Koch, I., Hoffmann, P., and Marron, J. S. (2014), “Proteomics Profiles from Mass Spectrometry,” Electronic Journal of Statistics, 8, 1703–1713.
  • Kurtek, S. (2017), “A Geometric Approach to Pairwise Bayesian Alignment of Functional Data Using Importance Sampling,” Electronic Journal of Statistics, 11, 502–531.
  • Kurtek, S., and Bharath, K. (2015), “Bayesian Sensitivity Analysis with the Fisher–Rao Metric,” Biometrika, 102, 601–616.
  • Kurtek, S., Srivastava, A., Klassen, E., and Ding, Z. (2012), “Statistical Modeling of Curves Using Shapes and Related Features,” Journal of the American Statistical Association, 107, 1152–1165.
  • Kurtek, S., Srivastava, A., and Wu, W. (2011), “Signal Estimation Under Random Time-Warpings and Nonlinear Signal Alignment,” in Neural Information Processing Systems (NIPS), pp. 675–683.
  • Liu, X., and Müller, H. G. (2004), “Functional Convex Averaging and Synchronization for Time-warped Random Curves,” Journal of the American Statistical Association, 99, 687–699.
  • Marron, J. S., Ramsay, J. O., Sangalli, L. M., and Srivastava, A. (2015), “Functional Data Analysis of Amplitude and Phase Variation,” Statistical Science, 30, 468–484.
  • Moore, J. K., Hnat, S. K., and van den Bogert, A. J. (2015), “An Elaborate Dataset on Human Gait and the Effect of Mechanical Perturbations,” PeerJ, 3, e918.
  • Raket, L. L., Sommer, S., and Markussen, B. (2014), “A Nonlinear Mixed-effects Model for Simultaneous Smoothing and Registration of Functional Data,” Pattern Recognition Letters, 38, 1–7.
  • Ramsay, J. O. (2000), “Functional Components of Variation in Handwriting,” Journal of the American Statistical Association, 95, 9–15.
  • Ramsay, J. O., Gribble, P., and Kurtek, S. (2014), “Description and Processing of Functional Data Arising from Juggling Trajectories,” Electronic Journal of Statistics, 8, 1811–1816.
  • Ramsay, J. O., and Li, X. (1998), “Curve Registration,” Journal of the Royal Statistical Society, Series B, 60, 351–363.
  • Ramsay, J. O., and Silverman, B. W. (2002), Applied Functional Data Analysis: Methods and Case Studies (1st ed.), New York: Springer-Verlag.
  • Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis (2nd ed.), New York: Springer-Verlag.
  • Ramsay, J. O., Wickham, H., Graves, S., and Hooker, G. (2014), Functional Data Analysis, R Package Version 2.4.4.
  • Sadeghi, H., Allard, P., Shafie, K., Mathieu, P. A., Sadeghi, S., Prince, F., and Ramsay, J. O. (2000), “Reduction of Gait Data Variability Using Curve Registration,” Gait & posture, 12, 257–264.
  • Sangalli, L. M., Secchi, P., and Vantini, S. (2014), “AneuRisk65: A Dataset of Three-dimensional Cerebral Vascular Geometries,” Electronic Journal of Statistics, 8, 1879–1890.
  • Senin, P. (2008), Dynamic Time Warping Algorithm Review, Honolulu, HI: Information and Computer Science Department, University of Hawaii at Manoa Honolulu.
  • Shorter, K. A., Polk, J. D., Rosengren, K. S., and Hsiao-Wecksler, E. T. (2008), “A New Approach to Detecting Asymmetries in Gait,” Clinical Biomechanics, 23, 459–467.
  • Silverman, B. W. (1995), “Incorporating Parametric Effects into Functional Principal Components Analysis,” Journal of the Royal Statistical Society, 57, 673–689.
  • Simon, S. R. (2004), “Quantification of Human Motion: Gait Analysis-Benefits and Limitations to its Application to Clinical Problems,” Journal of Biomechanics, 37, 1869–1880.
  • Srivastava, A., Jermyn, I., and Joshi, S. (2007), “Riemannian Analysis of Probability Density Functions with Applications in Vision,” in IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8.
  • Srivastava, A., Klassen, E., Joshi, S. H., and Jermyn, I. H. (2011a), “Shape Analysis of Elastic Curves in Euclidean Spaces,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 33, 1415–1428.
  • Srivastava, A., Wu, W., Kurtek, S., Klassen, E., and Marron, J. S. (2011b), “Registration of Functional Data Using Fisher-Rao Metric,” arXiv preprint, arXiv:1103.3817.
  • Stuart, A. M. (2010), “Inverse Problems: A Bayesian Perspective,” Acta Numerica, 19, 451–559.
  • Tang, R., and Müller, H. G. (2008), “Pairwise Curve Synchronization for Functional Data,” Biometrika, 95, 875–889.
  • Telesca, D., and Inoue, L. Y. T. (2008), “Bayesian Hierarchical Curve Registration,” Journal of the American Statistical Association, 103, 328–339.
  • Tucker, J. D. (2016), Elastic Functional Data Analysis, R Package Version 1.6.0.
  • Tuddenham, R. D., and Snyder, M. M. (1954), “Physical Growth of California Boys and Girls from Birth to Eighteen Years,” Publications in Child Development at University of California, Berkeley, 1, 183.
  • van den Bogert, A. J., Geijtenbeek, T., Even-Zohar, O., Steenbrink, F., and Hardin, E. C. (2013), “A Real-Time System for Biomechanical Analysis of Human Movement and Muscle Function,” Medical & Biological Engineering & Computing, 51, 1069–1077.
  • Wang, K., and Gasser, T. (1997), “Alignment of Curves byDynamic Time Warping,” The Annals of Statistics, 25, 1251–1276.
  • Winter, D. A. (1984), “Kinematic and Kinetic Patterns in Human Gait: Variability and Compensating Effects,” Human Movement Science, 3, 51–76.
  • Wu, W., Hatsopoulos, N. G., and Srivastava, A. (2014), “Introduction to Neural Spike Train Data for Phase-Amplitude Analysis,” Electronic Journal of Statistics, 8, 1759–1768.

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