Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Tucker, James Derek; Shand, Lyndsay; Chowdhary, Kamaljit Singh Kenny

doi:10.1016/j.csda.2021.107298

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Journal Article · Tue Jun 08 00:00:00 EDT 2021 · Computational Statistics and Data Analysis (Print)

DOI:https://doi.org/10.1016/j.csda.2021.107298· OSTI ID:1798142

Tucker, James Derek ^[1]; Shand, Lyndsay ^[1]; Chowdhary, Kamaljit Singh Kenny ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1798142

Alternate ID(s):: OSTI ID: 1788094

Report Number(s):: SAND--2021-6871J; 696769

Journal Information:: Computational Statistics and Data Analysis (Print), Journal Name: Computational Statistics and Data Analysis (Print) Vol. 163; ISSN 0167-9473

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

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