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A multiresolution approach to time warping achieved by a Bayesian prior–posterior transfer fitting strategy


Gerda Claeskens, Department of Operations Research and Business Statistics and Leuven Statistics Research Center, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium.


Summary.  Warping is an approach to the reduction and analysis of phase variability in functional observations, by applying a smooth bijection to the function argument. We propose a natural representation of warping functions in terms of a new type of elementary functions named ‘warping component functions’, or ‘warplets’, which are combined into the warping function by composition. The inverse warping function is trivial and explicit to obtain. A sequential Bayesian estimation strategy is introduced which fits a series of models and transfers the posterior of the previous fit into the prior of the next fit. Model selection is based on a warping analogue to wavelet thresholding, combined with Bayesian inference.