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Abstract:
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Warping functions are an intrinsic ingredient of Functional Data Analysis, because observed functions or image often need to be registered, or warped, to fit well to one another. Current approaches to the estimation of warping functions all work by modeling the function in terms of the displacements of particular points in time or space. This is not the natural approach, because warping functions are members of the group of transformations of time or space onto itself, rather than just functions. The approach I shall describe and discuss models warping functions as the composition of warplets, which are localized deformations of the time axis or image space. The order in which the warplets are composed matters, but this is something easily handled by reversible jump MCMC.
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