Theses and Dissertations

Date of Award

5-2024

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Statistics and Data Science

First Advisor

George P. Yanev

Second Advisor

Tamer F. Oraby

Third Advisor

Santanu Chakraborty

Abstract

The Generalized Poisson distribution is useful in modeling epidemiological processes as a branching stochastic processes problem. Our goal is to construct accurate and reliable estimators for the reproduction number (R0) (i.e., the number of secondary infections), particularly in the context of disease outbreaks modeled by a Galton-Watson process. Towards this goal, we construct the classical Bayes estimator, the Maximum Likelihood estimator, and the Empirical Bayes (EB) estimator under the Square Error Loss function in Chapter II. We prove that the Empirical Bayes estimator is asymptotically optimal and estimate the rate of convergence. We then proceed to monotonize the Empirical Bayes estimator in Chapter III using the Van Houwelingen method [22] and the Isotonic Regression method [3], then introduced the concept of the risk and regret risk associated with our estimators. For the numerical study in Chapter IV we assume a Poisson distribution for the reproduction number and that the initial number of infected individuals follows a Poisson distribution. Simulation results indicate that the empirical estimator suffers from "jumpiness", hence the need for monotonization. We then compare the regret risks of each of the estimators and find out that the monotonized estimate outperforms the others.

Comments

Copyright 2024 Alberta Araba Johnson.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/pqdtglobal1/dissertations-theses/bayesian-estimation-reproduction-numbers/docview/3085283692/sem-2?accountid=7119

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