Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data

Matuk, James; Bharath, Karthik; Chkrebtii, Oksana; Kurtek, Sebastian

Abstract

In many applications, smooth processes generate data that are recorded under a variety of observational regimes, including dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observational regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability using two strategies: a data-driven approach that defines an empirical basis for the amplitude subspace based on training data, and a shape-restricted approach when the relative location and number of extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using multiple simulation studies and real applications.

Citation

Matuk, J., Bharath, K., Chkrebtii, O., & Kurtek, S. (2022). Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data. Journal of the American Statistical Association, 117(540), 1964-1980. https://doi.org/10.1080/01621459.2021.1893179

• Journal Article Type: Article
• Acceptance Date: Feb 9, 2021
• Online Publication Date: Mar 29, 2021
• Publication Date: 2022
• Deposit Date: Feb 21, 2021
• Publicly Available Date: Mar 30, 2022
• Journal: Journal of the American Statistical Association
• Print ISSN: 0162-1459
• Electronic ISSN: 1537-274X
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• Volume: 117
• Issue: 540
• Pages: 1964-1980
• DOI: https://doi.org/10.1080/01621459.2021.1893179
• Keywords: function estimation; function registration; amplitude and phase variability; square- root velocity function; Bayesian inference
• Public URL: https://nottingham-repository.worktribe.com/output/5344241
• Publisher URL: https://www.tandfonline.com/doi/abs/10.1080/01621459.2021.1893179
• Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 29/03/2021, available online: https://www.tandfonline.com/doi/abs/10.1080/01621459.2021.1893179?journalCode=uasa20