Bayesian wavelet-packet historical functional linear models

Meyer Mark J.; Malloy Elizabeth J.; Coull Brent A.

摘要

Historical functional linear models (HFLMs) quantify associations between a functional predictor and functional outcome where the predictor is an exposure variable that occurs before, or at least concurrently with, the outcome. Prior work on the HFLM has largely focused on estimation of a surface that represents a time-varying association between the functional outcome and the functional exposure. This existing work has employed frequentist and spline-based estimation methods, with little attention paid to formal inference or adjustment for multiple testing and no approaches that implement wavelet bases. In this work, we propose a new functional regression model that estimates the time-varying, lagged association between a functional outcome and a functional exposure. Building off of recently developed function-on-function regression methods, the model employs a novel use the wavelet-packet decomposition of the exposure and outcome functions that allows us to strictly enforce the temporal ordering of exposure and outcome, which is not possible with existing wavelet-based functional models. Using a fully Bayesian approach, we conduct formal inference on the time-varying lagged association, while adjusting for multiple testing. We investigate the operating characteristics of our wavelet-packet HFLM and compare them to those of two existing estimation procedures in simulation. We also assess several inference techniques and use the model to analyze data on the impact of lagged exposure to particulate matter finer than 2.5 mu g, or PM2.5, on heart rate variability in a cohort of journeyman boilermakers during the morning of a typical day's shift.

机译：历史功能线性模型（HFLMS）量化功能预测器和功能结果之间的关联，其中预测器是曝光变量，其在结果之前或至少与结果同时发生。 HFLM的前程在很大程度上重点关注估计具有功能结果和功能暴露之间的时变关的表面。这项现有的工作已经采用了频繁的频率和基于样条曲线的估计方法，几乎没有注意到正式推理或调整多重测试，没有实现小波底座的方法。在这项工作中，我们提出了一种新的功能回归模型，估计功能结果和功能暴露之间的时变滞后关联。建立近期开发的功能函数回归方法，该模型采用了一种新颖的使用小波包分解的曝光和结果函数，使我们能够严格执行曝光和结果的时间顺序，这是不可能存在的基于小波的功能模型。使用完全贝叶斯方法，我们对时变滞后关联进行正式推断，同时调整多次测试。我们调查我们的小波包HFLM的操作特性，并将它们与模拟中的两个现有估算程序的操作特性进行比较。我们还评估了几种推理技术，并使用模型分析了滞后暴露于颗粒物质的影响，比2.5 mu g，或pm2.5，在典型的一天的早晨，在历史悠久的一天的历史型锅炉中的心率变异上转移。

Bayesian wavelet-packet historical functional linear models

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