The Mathematical Institute, University of Oxford, Eprints Archive

Sequential inverse problems Bayesian principles and the
logistic map example

Duan, L. and Farmer, C. L. and Moroz, I. M. (2010) Sequential inverse problems Bayesian principles and the
logistic map example.
In: ICNAAM 2010. (Submitted)

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Abstract

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

Item Type:Conference or Workshop Item (Paper)
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1005
Deposited By:Peter Hudston
Deposited On:28 Oct 2010 14:40
Last Modified:09 Feb 2012 15:56

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