Statistics and Data Science Seminar

— 5:00pm

Location:
In Person - Gates Hillman 4307

Speaker:
SATARUPA BHATTACHARJEE , Postdoctoral Scholar, Department o Statistics, Pennsylvania State University
https://satarupa3671.github.io/about/

Geodesic Mixed Effects Models for repeatedly Observed/Longitudinal Random Objects

Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in 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 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. 

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Satarupa Bhattacharjee is a Postdoctoral Scholar in the Department of Statistics at Pennsylvania State University, working with Prof. Bing Li and Prof. Lingzhou Xue.  I received my PhD in Statistics at UC Davis advised by Prof.Hans-Georg Müller in September 2022.  My 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 genetics data.

Event Website:
https://www.cmu.edu/dietrich/statistics-datascience/events/index.html

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