Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.
Original languageEnglish (US)
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010
Number of pages1070
StatePublished - 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-10-07
Acknowledged KAUST grant number(s): KUK-C1-013-04
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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


Dive into the research topics of 'Sequential Inverse Problems Bayesian Principles and the Logistic Map Example'. Together they form a unique fingerprint.

Cite this