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PDE-based Bayesian hierarchical modeling for event spread, with application to COVID-19 infection

Thesis type
(Project) M.Sc.
Date created
2022-04-20
Authors/Contributors
Author: Cen, Mengqi
Abstract
Motivated partly by the ongoing COVID-19 pandemic, this project aims to develop a tool for investigating spatio-temporal spread of events. We use the records of American coronavirus disease cases over time from The New York Times to motivate and illustrate the methodological development. Wikle (2003) considers a Bayesian hierarchical model based on a diffusion-reaction equation with a space-varying diffusion rate to describe the latent spatiotemporal 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. A Markov chain Monte Carlo (MCMC) method is applied to obtain samples from the posterior distribution 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 USA, and the growth rate and the 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.
Document
Identifier
etd21927
Copyright statement
Copyright is held by the author(s).
Permissions
This thesis may be printed or downloaded for non-commercial research and scholarly purposes.
Supervisor or Senior Supervisor
Thesis advisor: Hu, X. Joan
Language
English
Download file Size
input_data\22430\etd21927.pdf 2.44 MB

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