Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

Embargo End Date
2022-10-06

Type
Conference Paper

Authors
Duan, Lian
Farmer, Chris L.
Moroz, Irene M.

KAUST Grant Number
KUK-C1-013-04

Date
2010

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.

Citation
Duan, L., Farmer, C. L., Moroz, I. M., Simos, T. E., Psihoyios, G., & Tsitouras, C. (2010). Sequential Inverse Problems Bayesian Principles and the Logistic Map Example. doi:10.1063/1.3497821

Acknowledgements
This publication was based on work supported in part by Award No KUK-C1-013-04 , made by King Abdullah University of Science and Technology (KAUST).

DOI
10.1063/1.3497821

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