Theses and Dissertations

Date of Award

8-2021

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. George P. Yanev

Second Advisor

Dr. Hansapani Rodrigo

Third Advisor

Dr. Tamer F. Oraby

Abstract

Epidemic outbreaks can be modelled as a branching process in which the total progeny or outbreak size, follows a Borel-Tanner (BT) distribution. Following a procedure described by Liang (2009), we construct empirical Bayes estimates for when the initial number of infected is a specified value r. Following the construction, we then simulate data and perform a numerical study, assuming BT distribution for the parameter θ, the reproduction number, with an initial outbreak size of three. Simulation results indicate that the empirical estimator suffers from “jumpiness.” We then proceed to monotonize the empirical estimate via a method outlined by Houwelingen (1979). We then compared the regret risks of each of the estimators and found that the monotonized estimate is the superior estimator for θ. Testing for different values of b under the linex loss function seems to indicate negative b values produce better monotonized estimates. Lastly, we constructed an empirical Bayes estimate for the case when the initial number of infected is a Poisson random variable.

Comments

Copyright 2021 Elijah Lee Hight. All Rights Reserved.

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