TY - GEN
T1 - Sequential Inverse Problems Bayesian Principles and the Logistic Map Example
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 -