Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations

Bayesian parameter estimation in coupled ordinary differential equations (ODEs) is challenging due to the high computational cost of numerical integration. In gradient matching a separate data model is introduced with the property that its gradient can be calculated easily. Parameter estimation is achieved by requiring consistency between the gradients computed from the data model and those specified by the ODE. We propose a Gaussian process model that directly links state derivative information with system observations, simplifying previous approaches and providing a natural generative model.