Bayesian Parameter Estimation for Nonlinear Dynamics Using Sensitivity Analysis

Bayesian Parameter Estimation for Nonlinear Dynamics Using Sensitivity Analysis

Yi Chou, Sriram Sankaranarayanan

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
Main track. Pages 5708-5714. https://doi.org/10.24963/ijcai.2019/791

We investigate approximate Bayesian inference techniques for nonlinear systems described by ordinary differential equation (ODE) models. In particular, the approximations will be based on set-valued reachability analysis approaches, yielding approximate models for the posterior distribution. Nonlinear ODEs are widely used to mathematically describe physical and biological models. However, these models are often described by parameters that are not directly measurable and have an impact on the system behaviors. Often, noisy measurement data combined with physical/biological intuition serve as the means for finding appropriate values of these parameters. Our approach operates under a Bayesian framework, given prior distribution over the parameter space and noisy observations under a known sampling distribution. We explore subsets of the space of model parameters, computing bounds on the likelihood for each subset. This is performed using nonlinear set-valued reachability analysis that is made faster by means of linearization around a reference trajectory. The tiling of the parameter space can be adaptively refined to make bounds on the likelihood tighter. We evaluate our approach on a variety of nonlinear benchmarks and compare our results with Markov Chain Monte Carlo and Sequential Monte Carlo approaches.
Keywords:
Uncertainty in AI: Approximate Probabilistic Inference
Machine Learning: Learning Generative Models