Graduate Students Seminar

Session Chair:    Alexandra Hudson
Discussant:         Dr. Thomas Mathew

Speaker 1: Lara Scott

Title Multiscale Modeling of Chemoattractant-Guided Collective Cell Migration in the Drosophila Egg Chamber

Abstract
Collective cell migration is essential in wound healing, development, immune response, and cancer metastasis, yet linking molecular signaling to coordinated tissue-level motion remains an open challenge. My research develops multiscale mathematical models that couple chemoattractant signaling with cell mechanics to understand how collective migration emerges from local interactions. Using Drosophila melanogaster egg chambers, I strive to combine imaging-derived geometries with reaction-diffusion PDEs and a force-based agent-based model, where cell boundaries evolve under mechanical and migratory forces. This framework links experimentally measured tissue structure to mechanochemical dynamics, enabling investigation of how chemoattractant gradients influence migration patterns, cluster stability, and collective behavior.

Speaker 2: Soumadeep Bhowmick

Title Benchmarking Priors: A Fully Bayesian Approach to Small Area Benchmarking

Abstract
We develop a new class of priors for small-area models that allows a full Bayesian treatment under strict external benchmarking constraints. The prior is fully supported on the constrained parameter set defined by the benchmarking constraints and thereby provides a proper constrained posterior that is also supported on the restricted set. The posterior naturally constrains small-area estimates to conform to the benchmarking values at the aggregate level. Also, it facilitates valid uncertainty quantification using credible sets that are fully contained within the constrained set. This novel framework has a wide range of applicability, ranging from the standard Gaussian Fay-Herriot model to more general Fay-Herriot models, such as robust Fay-Herriot models, where the sampling errors are distributed as multivariate t, or Fay-Herriot models where there is a complex nonlinear relationship between the area means and the covariates. We illustrate the usefulness of the proposed methodology using simulation experiments as well as the 2019 American Community Survey Public Use Microdata Sample data from Maryland on Per Capita Income. The numerical results reaffirm the advantages of the proposed benchmarking priors.