Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions also have multiple optimal solutions, not addressed in current literature. In this paper, flexible Bayesian approach presented, appropriately accounts noise the without any pre-smoothing required. Additionally, by running parallel MCMC chains, method account alignments via multi-modal posterior distribution warping functions. To efficiently sample functions, relies on modification standard Hamiltonian Monte Carlo well-defined infinite-dimensional Hilbert space. This applied both simulated and real sets show its efficiency handling noisy successfully accounting posterior; characterizing uncertainty surrounding