Many disciplines of science involve mathematical modeling of phenomena with dynamic systems. The general trend is to model complex dynamical systems through the use of differential equations. These differential equation models often have non-measurable parameters such as planetary masses or chemical reaction rates. The “forward-problem” of simulation consists of solving the differential equations for a given set of parameters. The “inverse problem” or parameter estimation in this case, is the process of using data to determine these model parameters. The inverse problem has been heavily studied in certain fields as has already been presented in the case of Geophysics in the previous JuliaCon with jInv.jl, additionally because of its applications in different fields like systems biology, HIV-AIDS study, and drug dosage estimation it presents a good avenue for further research. This talk will introduce the attendees to the parameter estimation problems and show how to use DiffEqBayes.jl to perform Bayesian parameter estimation via techniques like Markov Chain Monte Carlo, Stochastic Approximation Expectation Maximization algorithm and Maximum A Posteriori estimation. Through this talk attendees will learn the purpose of parameter estimation and leave with knowledge of tooling for estimating parameters of differential equation models created using Julia’s differential equations suite.
