MODELING TRAJECTORIES USING FUNCTIONAL LINEAR DIFFERENTIAL EQUATIONS.

IF 1.3 4区 数学 Q2 STATISTICS & PROBABILITY
Annals of Applied Statistics Pub Date : 2024-12-01 Epub Date: 2024-10-31 DOI:10.1214/24-aoas1943
Julia Wrobel, Britton Sauerbrei, Eric A Kirk, Jian-Zhong Guo, Adam Hantman, Jeff Goldsmith
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引用次数: 0

Abstract

We are motivated by a study that seeks to better understand the dynamic relationship between muscle activation and paw position during locomotion. For each gait cycle in this experiment, activation in the biceps and triceps is measured continuously and in parallel with paw position as a mouse trotted on a treadmill. We propose an innovative general regression method that draws from both ordinary differential equations and functional data analysis to model the relationship between these functional inputs and responses as a dynamical system that evolves over time. Specifically, our model addresses gaps in both literatures and borrows strength across curves estimating ODE parameters across all curves simultaneously rather than separately modeling each functional observation. Our approach compares favorably to related functional data methods in simulations and in cross-validated predictive accuracy of paw position in the gait data. In the analysis of the gait cycles, we find that paw speed and position are dynamically influenced by inputs from the biceps and triceps muscles and that the effect of muscle activation persists beyond the activation itself.

利用函数线性微分方程建模轨迹。
我们的动机是一项旨在更好地理解运动过程中肌肉激活和爪子位置之间的动态关系的研究。在本实验的每个步态周期中,连续测量二头肌和三头肌的激活,并与小鼠在跑步机上小跑时的脚掌位置平行。我们提出了一种创新的一般回归方法,该方法利用常微分方程和函数数据分析来模拟这些函数输入和响应之间的关系,作为一个随时间演变的动态系统。具体来说,我们的模型解决了两篇文献中的空白,并借用了曲线间的强度,同时估计所有曲线上的ODE参数,而不是单独建模每个功能观测值。我们的方法在模拟和步态数据中交叉验证的爪子位置预测准确性方面优于相关的功能数据方法。在步态周期的分析中,我们发现爪子的速度和位置受到二头肌和三头肌输入的动态影响,并且肌肉激活的影响持续存在于激活本身之外。
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来源期刊
Annals of Applied Statistics
Annals of Applied Statistics 社会科学-统计学与概率论
CiteScore
3.10
自引率
5.60%
发文量
131
审稿时长
6-12 weeks
期刊介绍: Statistical research spans an enormous range from direct subject-matter collaborations to pure mathematical theory. The Annals of Applied Statistics, the newest journal from the IMS, is aimed at papers in the applied half of this range. Published quarterly in both print and electronic form, our goal is to provide a timely and unified forum for all areas of applied statistics.
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