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Using Computational Bayesian Statistics To Analyze Parameters In A Differential Equation Model, Jacob Menix
Using Computational Bayesian Statistics To Analyze Parameters In A Differential Equation Model, Jacob Menix
Mahurin Honors College Capstone Experience/Thesis Projects
The purpose of this project is to use Bayesian statistics to analyze values of parameters for a previously developed system of differential equations which describes the healing process of diabetic foot ulcers. The model describes the relationships between matrix metalloproteinases (MMPs), their inhibitors (TIMPs), and extracellular matrix (ECM). A Bayesian approach is used when the availability of data is sparse, as it is in this case. Delayed Rejection Adaptive Metropolis (DRAM), a MATLAB implementation of a Metropolis-Hastings algorithm, is used to estimate parameters. This approach with the individual patient data allows us to estimate and compare parameters and their pairwise …