- Time series analysis
- Bayesian models
- Statistical models for brain images and signals
Current research projects:
NSF SES-1853210 Statistical Approaches for Complex Multi-Dimensional Data
This research project will develop models and statistical tools for the analysis of complex multi-dimensional temporal data. Data with these characteristics commonly arise in fields such as neuroscience, the environmental sciences, and economics. Currently, there are limitations with the statistical tools available to analyze these data, particularly in neuroimaging. Some of the commonly used methods are either not able to adequately capture the complex structure underlying these data or are computationally expensive and only practically feasible in very low-dimensional settings. This project will result in improved methods that are general and therefore applicable to the analysis of data from a variety of fields. New educational and training opportunities will be provided to graduate students pursuing research at the interface between statistics and other areas such as neuroscience and the environmental sciences. Open-source software that implements the new statistical tools will be developed and made publicly available.
The research project will develop new multivariate Bayesian dynamic models for joint analysis and forecasting of a collection of non-stationary time series data. These models and related computational tools will lead to joint and fast inference on the time-varying spectral features that characterize each individual time series, as well as inference on the time-frequency relationships across the time series components in the set. Dynamic hierarchical models for analysis of multiple time series also will be developed. The hierarchical approach will borrow strength across multiple time series to make accurate inferences on their common underlying time-frequency structure. Tools for sparsity and dimension reduction in these multi-dimensional temporal model settings will be developed and implemented. The investigator will apply the new methods to brain imaging data, multi-channel electroencephalogram data, fMRI data, and multivariate environmental data.
Collaborators: James Ackman MCD Biology UCSC
Students currently affiliated with the project:
- Wenjie Zhao (PhD Candidate in Statistics UCSC)
- With Prof. Rajarshi Guhaniyogi (Statistics, UCSC) and Statistics PhD student Dan Spencer, we have a research collaboration to develop Bayesian tensor regression approaches for neuroimaging data. Dan received a student award at the 2019 Statistics in Imaging Conference.
- With Cheng-Han Yu, Hernando Ombao and Daniel Rowe we have developed models for analyzing complex-valued fMRI
- With Annalisa Cadonna and Thanasis Kottas we have developed flexible models developed models for spectral analysis of multiple time series.
- With Raquel Barata and Bruno Sanso we are developing models for detection and forecasting of atmospheric rivers.