Dataset Information

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

ABSTRACT: 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.

SUBMITTER: Zhu B

PROVIDER: S-EPMC3128649 | biostudies-literature | 2011 Dec

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

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

Zhu Bin B Song Peter X-K PX Taylor Jeremy M G JM

Biometrics 20110318 4

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 straig ...[more]

PMID: 21418053

Similar Datasets

Project description:There is strong interest in investigating both functional connectivity (FC) using functional magnetic resonance imaging (fMRI) and structural connectivity (SC) using diffusion tensor imaging (DTI). There is also emerging evidence of correspondence between functional and structural pathways within many networks (Greicius, et al., 2009; Skudlarski et al., 2008; van den Heuvel et al., 2009), although some regions without SC exhibit strong FC (Honey et al., 2008). These findings suggest that FC may be mediated by (direct or indirect) anatomical connections, offering an opportunity to supplement fMRI data with DTI data when determining FC. We develop a novel statistical method for determining FC, called anatomically weighted FC (awFC), which combines fMRI and DTI data. Our awFC approach implements a hierarchical clustering algorithm that establishes neural processing networks using a new distance measure consisting of two components, a primary functional component that captures correlations between fMRI signals from different regions and a secondary anatomical weight reflecting probabilities of SC. The awFC approach defaults to conventional unweighted clustering for specific parameter settings. We optimize awFC parameters using a strictly functional criterion, therefore our approach will generally perform at least as well as an unweighted analysis, with respect to intracluster coherence or autocorrelation. AwFC also yields more informative results since it provides structural properties associated with identified functional networks. We apply awFC to two fMRI data sets: resting-state data from 6 healthy subjects and data from 17 subjects performing an auditory task. In these examples, awFC leads to more highly autocorrelated networks than a conventional analysis. We also conduct a simulation study, which demonstrates accurate performance of awFC and confirms that awFC generally yields comparable, if not superior, accuracy relative to a standard approach.

Dataset Information

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

Publications

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

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure