2024-06-24T20:52:33Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1719272022-12-21T00:19:18Zoai_pmh:repo_items171927
https://hdl.handle.net/2286/R.2.N.171927
http://rightsstatements.org/vocab/InC/1.0/
All Rights Reserved
2022
132 pages
Doctoral Dissertation
Academic theses
Text
eng
Martinez Rivera, Wilmer Osvaldo
Fricks, John
Reiser, Mark
Zhou, Shuang
Cheng, Dan
Lan, Shiwei
Arizona State University
Partial requirement for: Ph.D., Arizona State University, 2022
Field of study: Statistics
Tracking disease cases is an essential task in public health; however, tracking the number of cases of a disease may be difficult not every infection can be recorded by public health authorities. Notably, this may happen with whole country measles case reports, even such countries with robust registration systems. Eilertson et al. (2019) propose using a state-space model combined with maximum likelihood methods for estimating measles transmission. A Bayesian approach that uses particle Markov Chain Monte Carlo (pMCMC) is proposed to estimate the parameters of the non-linear state-space model developed in Eilertson et al. (2019) and similar previous studies. This dissertation illustrates the performance of this approach by calculating posterior estimates of the model parameters and predictions of the unobserved states in simulations and case studies. Also, Iteration Filtering (IF2) is used as a support method to verify the Bayesian estimation and to inform the selection of prior distributions. In the second half of the thesis, a birth-death process is proposed to model the unobserved population size of a disease vector. This model studies the effect of a disease vector population size on a second affected population. The second population follows a non-homogenous Poisson process when conditioned on the vector process with a transition rate given by a scaled version of the vector population. The observation model also measures a potential threshold event when the host species population size surpasses a certain level yielding a higher transmission rate. A maximum likelihood procedure is developed for this model, which combines particle filtering with the Minorize-Maximization (MM) algorithm and extends the work of Crawford et al. (2014).
Statistics
Birth-death process
Non-linear state-space models
Particle MCMC
Threshold effect
Estimation for Disease Models Across Scales