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Abstract:
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We present a Bayesian method to register real-valued functional data by making inference on nonlinear time warping functions. We adopt transformations that are developed in a differential geometric framework to map the parameter space of warping functions into a linear space, which allows the definition of a Gaussian prior distribution. Avoiding discretization until the last step, we keep the infinite dimensionality of the warping functions when we write down the model. Draws from the posterior distribution of those warping functions are then obtained by a novel MCMC algorithm that utilizes the Karhunen-Loeve expansion to approximate a continuous function with a finite number of basis functions. Furthermore, we extend our method to simultaneously register more than two functions, in which case we also make inference on the underlying template curve that all of the observed functions are matched to. We apply our method to real data sets including growth rate curves in the Berkeley growth study and kinematic measurements obtained in a gait cycle study.
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