JSM 2013 Home
Online Program Home
My Program

Abstract Details

Activity Number: 297
Type: Topic Contributed
Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #307693
Title: Probabilistic Integration for Uncertainty Quantification in Differential Equation Models
Author(s): Oksana Chkrebtii*+ and Dave Campbell and Mark Girolami and Ben Calderhead
Companies: Simon Fraser University and Simon Fraser University and University College London and University College London
Keywords: uncertainty quantification ; Bayesian numerical analysis ; dynamic systems ; Bayesian inference
Abstract:

We present a Bayesian inferential framework based on a novel probabilistic formalism for solving general systems of analytically intractable differential equations. This approach provides an alternative to numerical integration for estimation of complex dynamic systems, avoiding the bias introduced when models are ill-conditioned or contain unmodeled functional uncertainty. Viewing solution estimation as an inference problem (Skilling, 1991; O'Hagan, 1992) allows us to quantify numerical uncertainty using the tools of Bayesian function estimation. We discuss useful properties of the probabilistic solution, highlight links with classical approaches, and develop a fully Bayesian framework for state and parameter inference from noisy observations of the states. Our approach is demostrated for ordinary and delay differential equation models, mixed boundary value problems, and the JAK-STAT biochemical signalling pathway delay-feedback mechanism.


Authors who are presenting talks have a * after their name.

Back to the full JSM 2013 program




2013 JSM Online Program Home

For information, contact jsm@amstat.org or phone (888) 231-3473.

If you have questions about the Continuing Education program, please contact the Education Department.

The views expressed here are those of the individual authors and not necessarily those of the JSM sponsors, their officers, or their staff.

ASA Meetings Department  •  732 North Washington Street, Alexandria, VA 22314  •  (703) 684-1221  •  meetings@amstat.org
Copyright © American Statistical Association.