Bayesian Registration of Functions and Curves

Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. We focus on two applications involving the classification of mo use vertebrae shape outlines and the alignment of mass spectrometry data in proteomics. The functions and curves of interest are represented using the recently introduced s quare root velocity function, which enables a warping invariant elastic distance to be calculated in a straightfor- ward manner. We distinguish between various spaces of interest: the original space, the ambient space after standardizing, and the quotient space after removing a group of transformations. Using Gaussian process models in the ambient space and Dirichlet priors for the warping functions, we explore Bayesian inference for curves and func- tions. Markov chain Monte Carlo algorithms are introduced for simulating from the posterior, including simulated tempering for multimodal posteriors. We also compare ambient and quotient space estimators for mean shape, and explain their frequent simi- larity in many practical problems using a Laplace approximation. A simulation study is carried out, as well as shape classification of the mouse vert ebra outlines and practical alignment of the mass spectrometry functions. MSC 2010 subject classifications: Primary 62F15, 62P10.