Brief Description of Interests

My research interests are centered in methodological developments in functional data analysis, nonparametric statistics, and graphical models. A significant focus of my recent work is on the analysis of samples of functional data that are density functions by incorporating geometric principles, in particular the Wasserstein metric of optimal transport. Applications of these methods are vast, including daily distributions of stock returns, post-intracerebral hemorrhage hematoma densities, and distributions of age-at-death for various countries. My projects in these areas involve a healthy mix of theory and application, with each lending interest and momentum to the other. A particular application area that has kept me occupied from my earliest research experiences as a graduate student is improving estimation of, and developing new methods to quantify, functional connectivity in the human (or, more recently, rat) brain. The data are usually available in the form of functional magnetic resonance imaging (fMRI) scans, and have been treated in scientific studies most often as network data, but also as functional data, distributional data, and covariance matrix-valued data. The data are rich but noisy, and pose a number of intriguing theoretical and computational challenges.

Funding

I am currently funded by two NSF grants:

• NSF IIS-2135859: Advanced Spatiotemporal Statistical Models for Quantification and Estimation of Functional Connectivity: Q-FunC (Jan. 2021-Dec. 2023)
• NSF DMS-2128589: Statistical Modelling of Multivariate Functional and Distributional Data (July 2018-June 2022)

Software

• robsel : Robust Selection Algorithm - An implementation of algorithms for estimation of the graphical lasso regularization parameter described in Cisneros-Velarde,P. , Petersen, A. and Oh, S.Y. (2020). Distributionally robust formulation and model selection for the graphical lasso, Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in PMLR 108:756-765.
• WRI : Wasserstein Regression Inference - An implementation of the methodologies described in Petersen, A., Liu, X. and Divani, A. A. (2021). Wasserstein F-tests and confidence bands for the Fréchet regression of density response curves, Annals of Statistics, 49(1), 590–611.
• fgm : Partial Separability and Functional Gaussian Graphical Models - Estimates a functional graphical model and a partially separable Karhunen-Loève decomposition for a multivariate Gaussian process as described in Zapata, J., Oh, S.Y. and Petersen, A. (2022+). Partial separability and functional graphical models for multivariate Gaussian processes, Biometrika, accepted
• fdadensity : Functional Data Analysis for Density Functions by Transformation to a Hilbert Space - An implementation of the methodology described in Petersen, A. and Müller, H.G. (2016). Functional data analysis for density functions by transformation to a Hilbert space, Annals of Statistics, 44(1), 183–218.