Stochastic functional data analysis: a diffusion model-based approach.

Published

Journal Article

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.

Full Text

Cited Authors

  • Zhu, B; Song, PX-K; Taylor, JMG

Published Date

  • December 2011

Published In

Volume / Issue

  • 67 / 4

Start / End Page

  • 1295 - 1304

PubMed ID

  • 21418053

Pubmed Central ID

  • 21418053

Electronic International Standard Serial Number (EISSN)

  • 1541-0420

International Standard Serial Number (ISSN)

  • 0006-341X

Digital Object Identifier (DOI)

  • 10.1111/j.1541-0420.2011.01591.x

Language

  • eng