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Abstract:
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In many applications, smooth functions generate data that are recorded under a variety of observation regimes, e.g. dense, sparse, or fragmented sampling, often contaminated with noise. Analysis of functional data is usually approached sequentially through estimation, registration, and inference. This approach lacks the ability to accommodate general observation regimes and formal uncertainty propagation. We propose a unified Bayesian framework for simultaneous registration and estimation, that is flexible enough to accommodate inference on individual functions under these observation regimes. Our ability to do this relies on the specification of strongly informative prior models on the amplitude component of a function. We provide two strategies for this choice: a data-driven approach that defines an empirical basis for the amplitude subspace based on available training data, or a shape-restricted approach when the relative location and number of local extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to accommodate amplitude and phase variability inherent in functional data and is validated on real and simulated datasets.
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