科学研究

Satarupa Bhattacharjee, currently a Postdoctoral Scholar in the Department of Statistics at Pennsylvania State University, working with Prof. Bing Li and Prof. Lingzhou Xue. She will be joining the University of Florida as an Assistant Professor in Statistics in the Fall of 2024. She received her PhD in Statistics at UC Davis advised by Prof. Hans-Georg Müller in 2022. She is on job market this year for faculty positions in US, and has got 20+ interview invitations, and most of the interviews turned to offers. 

 

Her primary research centers around analyzing functional and non-Euclidean data situated in general metric spaces, which we refer to as random objects, with examples in brain imaging data, networks, distribution valued data, and high-dimensional omics data.

Satarupa will first briefly share her intuition and ideas about preparing and delivering a well-connected presentation, as well as the tips when looking for academic jobs. She will then proceed to talk about developing a mixed-effects model for non-Euclidean or “random object'' data.

 

Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without either global linear or local linear (Riemannian) structure. In such settings the classical additive error model and distributional assumptions are unattainable. Due to the rapid advancement of technology, longitudinal data containing complex random objects, such as covariance matrices, data on Riemannian manifolds, and probability distributions are becoming more common. Addressing this challenge, we develop a mixed-effects regression for data in geodesic spaces, where the underlying mean response trajectories are geodesics in the metric space and the deviations of the observations from the model are quantified by perturbation maps or transports. A key finding is that the geodesic trajectories assumption for the case of random objects is a natural extension of the linearity assumption in the standard Euclidean scenario to the case of general geodesic metric spaces. Geodesics can be recovered from noisy observations by exploiting a connection between the geodesic path and the path obtained by global Fréchet regression for random objects. The effect of baseline Euclidean covariates on the geodesic paths is modeled by another Fréchet regression step. We study the asymptotic convergence of the proposed estimates and provide illustrations through simulations and real-data applications.