Bayesian Registration of Functions With a Gaussian Process Prior. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Lu, Yi; Herbei, Radu; Kurtek, Sebastian
• Is Part Of: Journal of computational and graphical statistics. Volume 26:Issue 4(2017)
• Page Start: 894
• Page End: 904
• Publication Date: 2017-10-02
• Subjects: Function registration -- Markov chain Monte Carlo -- Time warping; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2017.1336444
• Languages: English
• ISSNs: 1061-8600

Abstract

ABSTRACT: We present a Bayesian framework for registration of real-valued functional data. At the core of our approach is a series of transformations of the data and functional parameters, developed under a differential geometric framework. We aim to avoid discretization of functional objects for as long as possible, thus minimizing the potential pitfalls associated with high-dimensional Bayesian inference. Approximate draws from the posterior distribution are obtained using a novel Markov chain Monte Carlo (MCMC) algorithm, which is well suited for estimation of functions. We illustrate our approach via pairwise and multiple functional data registration, using both simulated and real datasets. Supplementary material for this article is available online.