Solution Uncertainty Quantification for Differential Equations

• Activity Number: 485 - Highlights from Bayesian Analysis
• Type: Invited
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Oksana A Chkrebtii* and David A Campbell and Ben Calderhead and Mark A Girolami
• Companies: The Ohio State University and Simon Fraser University and Imperial College London and University of Warwick
• Keywords: Bayesian numerical analysis ; uncertainty quantification ; differential equation models ; Gaussian processes ; Bayesian inference

Abstract

When models are defined implicitly by systems of differential equations without a closed form solution, small local errors in finite-dimensional solution approximations can propagate into large deviations from the true underlying state trajectory. Inference for such models relies on a likelihood approximation constructed around a numerical solution, which underestimates posterior uncertainty. This talk will introduce and discuss progress in a new formalism for modeling and propagating discretization uncertainty through the Bayesian inferential framework, allowing exact inference and uncertainty quantification for discretized differential equation models.