Title: Parameter Estimation for Dynamic Systems Models using Probabilistic Integration (Slides)
Abstract: Statistical inference on dynamic systems models is a central problem in the study of complex systems. Mathematical models of physical and biological processes such as chemical reactions, predator-prey dynamics, and gene regulation, consist of systems of high-dimensional coupled ordinary and partial differential equations that depend on large numbers of unknown parameters. Statistical techniques allow estimation of these parameters based on experimental or observational data for some subset of the state variables. Accurate parameter estimates are crucial for prediction and often have physical interpretations that allow us to learn more about the system dynamics. I will describe this as a problem in nonlinear regression and review some existing estimation approaches based on Nonlinear Least Squares and MCMC methods while pointing out common situations where these methods fail. Briefly, I will describe a new methodology for parameter estimation based on probabilistic solutions of systems of ordinary differential equations. This Bayesian framework incorporates solution uncertainty in the likelihood and thus in the inference process. Importantly, this model allows us to sample solution realizations together with system parameters, which leads to more flexibility in fitting the data, and an efficient way to explore possibly multimodal posterior distributions.