Hello we are Lena, Rachel, and Harry. This is our final course project for UBC CPSC 440/540 2021. We received a grade of 97/100.
Uncertainty quantification is a growing field in applied mathematics to deal withnoisy data in differential equation models. Approximate Bayesian computation is aclass of Bayesian methods originating from statistics that can be easily applied tosuch deterministic models to cope with uncertainty as well as intractable likelihoods.In this project, we implement three variants of approximate Bayesian methodsand apply them to estimate the parameters of the Susceptible-Infected-Recovered (SIR) epidemiological model and of the Lorenz system. We rigorously validate themethods via a simulation-based approach called Bayesian calibration, and analyzethe COVID-19 data using the SIR model.
The full report can be found here.