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