Modeling data in time and space : studies of irregularities, dependence structure and applications
- Author
- Dang, Huy
- Published
- [University Park, Pennsylvania] : Pennsylvania State University, 2023.
- Physical Description
- 1 electronic document
- Additional Creators
- Chiaromonte, Francesca
Access Online
- etda.libraries.psu.edu , Connect to this object online.
- Graduate Program
- Restrictions on Access
- Open Access.
- Summary
- This dissertation is a compilation of three research projects on the analysis of data in time and space. The first and second projects propose approaches for the analysis of longitudinal and spatio-temporal data that comprise irregularities, and the third project proposes an integrated approach for capturing the spatio-temporal dependence structure of spatially organized time series. In the first project, we propose a method that, combining an EM algorithm with penalized smoothing, can simultaneously estimate the smooth component and detect irregular spikes in a 1-dimensional signal. Imposing some assumptions on the error distribution, we study consistency of EM updates when some or all parameters are unknown. Robustness of the proposed method to assumptions violations is ascertained via simulations. The second project is motivated by a specific application in functional magnetic resonance imaging (fMRI); namely, head motion detection. Head motion can be viewed as an abrupt change in fMRI signals that are otherwise a smooth function of brain activities in time. By transforming the data to wavelet space, and studying the decay rate of wavelet coefficients across different scales, we are able to estimate the local smoothness of data in three dimensions (a 2-dimensional brain slice and time) and identify local irregularities. In the third project, we study the complex spatio-temporal dependence structure of cortical surface fMRI data. Specifically, we model the non-stationary dependence of activation patterns across the cortical surface via a stochastic differential equation prior. Moreover, we provide evidence of varying ranges of temporal dependence across different brain regions, and model such dependence as fractional Gaussian noise of varying Hurst parameters. The result is a fully integrated, efficient framework that considers spatial and temporal dependence structure simultaneously, and is computationally viable.
- Other Subject(s)
- Genre(s)
- Dissertation Note
- Ph.D. Pennsylvania State University 2023.
- Reproduction Note
- Microfilm (negative). 1 reel ; 35 mm. (IMR Digital 3-23-0019)
- Technical Details
- The full text of the dissertation is available as an Adobe Acrobat .pdf file ; Adobe Acrobat Reader required to view the file.
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