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.

摘要

在对每个实验单元的观察本质上都是功能性的实验中，通常情况是，除了沿水平轴的变化（高度或幅度变化）外，曲线中还存在横向位移/变形（称为相位变化） ）。与前者不同，后一种形式的可变性在进行推断时通常被视为一个令人讨厌的参数。因此，在功能数据分析中，通过称为曲线配准的过程对齐曲线来减少这种可变性是很常见的。通常，有关某些曲线特征出现的位置和时间的专业知识可用于指导曲线重新对齐。我们提出了一个贝叶斯模型，允许在使用高斯过程先验公式注册曲线时结合这些知识。这种新颖的方法利用了来自高斯过程的预测分布的插值特性，同时仍然保留了现代配准技术中的灵活性。我们详细介绍了计算策略，并通过模拟研究和膝动力生物力学分析说明了该方法的实用性。文章的补充材料可在线获取。