Stochastic Functional Data Analysis: A Diffusion Model-Based Approach
Article first published online: 18 MAR 2011
© 2011, The International Biometric Society
Volume 67, Issue 4, pages 1295–1304, December 2011
How to Cite
Zhu, B., Song, P. X.-K. and Taylor, J. M.G. (2011), Stochastic Functional Data Analysis: A Diffusion Model-Based Approach. Biometrics, 67: 1295–1304. doi: 10.1111/j.1541-0420.2011.01591.x
- Issue published online: 14 DEC 2011
- Article first published online: 18 MAR 2011
- Received January 2010. Revised January 2011. Accepted January 2011.
- Diffusion model;
- Euler approximation;
- Nonparametric regression;
- Simulation smoother;
- Stochastic differential equation;
- Stochastic velocity model
Summary This article presents a new modeling strategy in functional data analysis. We consider the problem of estimating an unknown smooth function given functional data with noise. The unknown function is treated as the realization of a stochastic process, which is incorporated into a diffusion model. The method of smoothing spline estimation is connected to a special case of this approach. The resulting models offer great flexibility to capture the dynamic features of functional data, and allow straightforward and meaningful interpretation. The likelihood of the models is derived with Euler approximation and data augmentation. A unified Bayesian inference method is carried out via a Markov chain Monte Carlo algorithm including a simulation smoother. The proposed models and methods are illustrated on some prostate-specific antigen data, where we also show how the models can be used for forecasting.