A Bayesian Model for Sparse Functional Data
- 26 February 2008
- journal article
- Published by Oxford University Press (OUP) in Biometrics
- Vol. 64 (1) , 54-63
- https://doi.org/10.1111/j.1541-0420.2007.00829.x
Abstract
Summary. We propose a method for analyzing data which consist of curves on multiple individuals, i.e., longitudinal or functional data. We use a Bayesian model where curves are expressed as linear combinations of B‐splines with random coefficients. The curves are estimated as posterior means obtained via Markov chain Monte Carlo (MCMC) methods, which automatically select the local level of smoothing. The method is applicable to situations where curves are sampled sparsely and/or at irregular time points. We construct posterior credible intervals for the mean curve and for the individual curves. This methodology provides unified, efficient, and flexible means for smoothing functional data.Keywords
This publication has 26 references indexed in Scilit:
- Rank-Based Estimation and Associated Inferences for Linear Models With Cluster Correlated ErrorsJournal of the American Statistical Association, 2009
- A default conjugate prior for variance components in generalized linear mixed models (comment on article by Browne and Draper)Bayesian Analysis, 2006
- Wavelet-based Functional Mixed ModelsJournal of the Royal Statistical Society Series B: Statistical Methodology, 2006
- Principal component models for sparse functional dataBiometrika, 2000
- Nonparametric smoothing estimates of time-varying coefficient models with longitudinal dataBiometrika, 1998
- Smoothing Spline Models for the Analysis of Nested and Crossed Samples of CurvesJournal of the American Statistical Association, 1998
- Mixed Effects Smoothing Spline Analysis of VarianceJournal of the Royal Statistical Society Series B: Statistical Methodology, 1998
- Nonparametric regression using Bayesian variable selectionJournal of Econometrics, 1996
- An Analysis of Paediatric CD4 Counts for Acquired Immune Deficiency Syndrome Using Flexible Random CurvesJournal of the Royal Statistical Society Series C: Applied Statistics, 1996
- A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by SplinesThe Annals of Mathematical Statistics, 1970