Semester of Graduation
Master of Applied Statistics (MApStat)
In the field of biology, mathematical models are increasingly used to address biological questions and the large data sets generated in experimental studies. Mathematical models traditionally are simplified and structured to be analytically tractable, but computing power allows for more complex, larger models. Bayesian statistics lends itself naturally to address parameter estimation problems in these large models. Bayesian statistical inference is utilized in this thesis to obtain parameter estimates from a sparse data set on populations in the HIV epidemic. Current estimates of the HIV epidemic indicate a decrease in the incidence of the disease in the undiagnosed subpopulation over the past 10 years. A lack of access to care, however, has not been considered when modeling the population. Populations at high risk for contracting HIV are twice as likely to lack access to reliable medical care. In this thesis, we consider three contributors to the HIV population dynamics: susceptible pool exhaustion, lack of access to care, and usage of anti-retroviral therapy (ART) by diagnosed individuals. An extant problem in the mathematical study of this system is deriving parameter estimates due to a portion of the population being unobserved. We approach this problem by looking at the proportional change in the infected subpopulations. We obtain estimates for the proportional change of the infected subpopulations using hierarchical Bayesian statistics. The estimated proportional change is used to derive epidemic parameter estimates for a system of stochastic differential equations (SDEs). Model fit is quantified to determine the best parametric explanation for the observed dynamics in the infected subpopulations. Parameter estimates derived using these methods provide interpretability and recovery of the system. Simulations suggest that the undiagnosed population may be larger than currently estimated without significantly affecting the population dynamics.
Dale, Renee, "Parameter estimation and optimization for biological mathematical models using Bayesian statistics" (2021). LSU Master's Theses. 5249.