Template Priors in Bayesian Curve Registration

Abstract

In experiments where observations on each experimental unit are functional in nature, it is often the case that, in addition to variability along the horizontal axis (height or amplitude variability), there are also lateral displacements/deformations in curves (referred to as phase variability). Unlike the former, the latter form of variability is often treated as a nuisance parameter when making inferences. Therefore, it is common in functional data analysis to reduce this variability by aligning curves through a process called curve registration. Often, expert knowledge regarding the location and time that certain curve features occur is available to guide the curve realignment. We propose a Bayesian model that permits incorporating this knowledge when registering curves using a Gaussian process prior formulation. This novel approach capitalizes on the interpolation property of predictive distributions from Gaussian processes while still preserving the flexibility found in modern registration techniques. We detail computational strategies and illustrate the utility of the method through a simulation study and an analysis of knee-power biomechanics. Supplementary materials for the article are available online.

Keywords:

• Bayesian hierarchical model
• Functional data analysis
• Gaussian process
• Landmarks
• Smoothing

Acknowledgments

The authors thank the editor, associate editor, and three anonymous referees for reviewing the article and providing valuable comments that greatly improved the quality of the article.

Supplementary Material

The online supplementary materials for this article contains additional results from the simulation studies and the power knee application, as well as computer codes that were employed to run the simulation studies. The R-package warptk, available on the first author’s Github page https://github.com/wzhorton/warptk/, contains codes for fitting the template prior method described in the article.