Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

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

doi:10.1063/1.3497821

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 proceeding › Conference contribution

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.

Original language	English (US)
Title of host publication	International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010
Publisher	AIP
Pages	1071-+
Number of pages	1070
DOIs	https://doi.org/10.1063/1.3497821
State	Published - 2010
Externally published	Yes

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.

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10.1063/1.3497821

Cite this

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title = "Sequential Inverse Problems Bayesian Principles and the Logistic Map Example",

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.",

author = "Lian Duan and Farmer, {Chris L.} and Moroz, {Irene M.}",

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.",

year = "2010",

doi = "10.1063/1.3497821",

language = "English (US)",

pages = "1071--+",

booktitle = "International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010",

publisher = "AIP",

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AU - Duan, Lian

AU - Farmer, Chris L.

AU - Moroz, Irene M.

N1 - 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.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/672175

UR - http://aip.scitation.org/doi/abs/10.1063/1.3497821

UR - http://www.scopus.com/inward/record.url?scp=79954453289&partnerID=8YFLogxK

U2 - 10.1063/1.3497821

DO - 10.1063/1.3497821

M3 - Conference contribution

SP - 1071-+

BT - International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010

PB - AIP

ER -

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

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