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.
E-mail: gerda.claeskens@econ.kuleuven.be


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.