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2016 Functional models for longitudinal data with covariate dependent smoothness
David K. Mensah, David J. Nott, Linda S. L. Tan, Lucy Marshall
Electron. J. Statist. 10(1): 527-549 (2016). DOI: 10.1214/16-EJS1113

Abstract

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.

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David K. Mensah. David J. Nott. Linda S. L. Tan. Lucy Marshall. "Functional models for longitudinal data with covariate dependent smoothness." Electron. J. Statist. 10 (1) 527 - 549, 2016. https://doi.org/10.1214/16-EJS1113

Information

Received: 1 July 2014; Published: 2016
First available in Project Euclid: 4 March 2016

zbMATH: 1332.62136
MathSciNet: MR3471987
Digital Object Identifier: 10.1214/16-EJS1113

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 1 • 2016
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