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Abstract:
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With advances in technology, functional data have become prevalent in various application domains. In many cases, the observed functions exhibit two distinct sources of variability, amplitude (y-axis) and phase (x-axis), which are extracted via a registration process. Under a Bayesian framework, registration is generally enabled via Markov chain Monte Carlo (MCMC). However, when new functional data is observed, the entire MCMC-based inferential process has to be repeated resulting in inefficient computation. To address these challenges, we introduce an online registration method for functional data, which recursively updates the inferential results when new functions are observed. The proposed approach utilizes sequential Monte Carlo sampling to update the posterior distributions of the mean amplitude and each observed function’s phase component. The updates are performed on a sequence of spaces of increasing dimension. Parallelization across multiple processors leads to efficient computation. We illustrate the performance of the proposed approach in high-dimensional and multimodal scenarios using simulated and real data.
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