Mengqi (Molly) Cen

Title: A PDE-Based Bayesian Hierarchical Model For Event Spread, with Application to Covid-19 Infection
Date: April 20, 2022
Time: 1:00 PM (PDT)
Location: Remote delivery

Abstract

Motivated by the current Covid-19 pandemic, this project aims to investigate event spatio-temporal spread.  We use the records of the American coronavirus disease cases from The New York Times to motivate and illustrate the methodological development. Wikle (2003) considers a Bayesian hierarchical model based on adiffusion-reaction equation with a space-varying diffusion rate to describe the latent spatio-temporal process underlying a collection of bird migration data. We extend the model by adding an advection term to account for the additional trend of the transmission, and considering time-varying reaction and advection terms. The Monte Carlo Markov Chain (MCMC) is applied to obtain samples from the posterior distributions of the parameters. The proposed approach is implemented via the Covid-19 data from The New York Times. The analysis results indicate that the diffusion rate is heterogeneous across the U.S., and the growth rate and advection velocity are time varying. We verify the findings from the analysis by simulation. The proposed approach appears robust to model misspecification and outperforms other approaches in the simulation settings.

Keywords: Advection; Diffusion; Disease Infection; Space State; Spatio-Temporal Pattern