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Functional models for longitudinal data with covariate dependent smoothness

机译：具有协变量相关平滑度的纵向数据的功能模型

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This paper considers functional models for longitudinal data with subject and group specific trends modelled using Gaussian processes. Fitting Gaussian process regression models is a computationally challenging task, and various sparse approximations to Gaussian processes have been considered in the literature to ease the computational burden. This manuscript builds on a fast non-standard variational approximation which uses a sparse spectral representation and is able to treat uncertainty in the covariance function hyperparameters. This allows fast variational computational methods to be extended to models where there are many functions to be estimated and where there is a hierarchical model involving the covariance function parameters. The main goal of this paper is to implement this idea in the context of functional models for longitudinal data by allowing individual specific smoothness related to covariates for different subjects. Understanding the relationship of smoothness to individual specific covariates is of great interest in some applications. The methods are illustrated with simulated data and a dataset of streamflow curves generated by a rainfall runoff model, and compared with MCMC. It is also shown how these methods can be used to obtain good proposal distributions for MCMC analyses.
机译：本文考虑纵向数据的功能模型，并使用高斯过程对特定主题和特定群体的趋势进行建模。拟合高斯过程回归模型是一项在计算上具有挑战性的任务，并且在文献中已经考虑了对高斯过程的各种稀疏近似，以减轻计算负担。该手稿基于使用稀疏频谱表示的快速非标准变分近似，并且能够处理协方差函数超参数中的不确定性。这允许将快速变分计算方法扩展到模型，在该模型中，有许多函数需要估计，并且在其中存在涉及协方差函数参数的层次模型。本文的主要目的是通过允许与不同主题的协变量相关的个别特定平滑度，在纵向数据功能模型的背景下实现这一想法。在某些应用中，了解平滑度与各个特定协变量的关系非常重要。用模拟数据和降雨径流模型生成的流量曲线数据集说明了这些方法，并与MCMC进行了比较。还显示了如何使用这些方法来为MCMC分析获得良好的建议分布。

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