# Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

@article{Tucker2021MultimodalBR, title={Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo}, author={J. D. Tucker and Lyndsay Shand and Kenny Chowdhary}, journal={Comput. Stat. Data Anal.}, year={2021}, volume={163}, pages={107298} }

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… Expand

#### Figures from this paper

#### One Citation

Registration for Incomplete Non-Gaussian Functional Data

- Mathematics
- 2021

Accounting for phase variability is a critical challenge in functional data analysis. To separate it from amplitude variation, functional data are registered, i.e., their observed domains are… Expand

#### References

SHOWING 1-10 OF 28 REFERENCES

Bayesian Registration of Functions With a Gaussian Process Prior

- Mathematics
- 2017

ABSTRACT We present a Bayesian framework for registration of real-valued functional data. At the core of our approach is a series of transformations of the data and functional parameters, developed… Expand

Geometric MCMC for infinite-dimensional inverse problems

- Mathematics, Computer Science
- J. Comput. Phys.
- 2017

This work combines geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches to speed up MCMC mixing times, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. Expand

Bayesian Registration of Functions and Curves

- Mathematics, Computer Science
- 2013

This work focuses on two applications involving the classification of mo use vertebrae shape outlines and the alignment of mass spectrometry data in proteomics, represented using the recently introduced quare root velocity function, which enables a warping invariant elastic distance to be calculated in a straightforward manner. Expand

Shape Analysis of Elastic Curves in Euclidean Spaces

- Mathematics, Computer Science
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- 2011

This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric and demonstrates a wrapped probability distribution for capturing shapes of planar closed curves. Expand

Generative models for functional data using phase and amplitude separation

- Computer Science, Mathematics
- Comput. Stat. Data Anal.
- 2013

This paper presents an approach that relies on separating the phase and amplitude of functional data, then modeling these components using joint distributions, and imposes joint probability models on principal coefficients of these components while respecting the nonlinear geometry of the phase representation space. Expand

Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data

- Computer Science, Mathematics
- 2019

Mathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)

Registration for exponential family functional data.

- Mathematics, Medicine
- Biometrics
- 2019

A novel method for separating amplitude and phase variability in exponential family functional data is introduced, andSimulations designed to mimic the application indicate that the proposed methods outperform competing approaches in terms of estimation accuracy and computational efficiency. Expand

A Geometric Approach to Visualization of Variability in Functional Data

- Computer Science, Mathematics
- 2017

This work uses a recent functional data analysis framework, based on a representation of functions called square-root slope functions, to decompose observed variation in functional data into three main components: amplitude, phase, and vertical translation. Expand

Amplitude and phase variation of point processes

- Mathematics
- 2016

We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation.… Expand