Accounting for Modelling Errors in Parameter Estimation Problems: The Bayesian Approximation Error Approach

  • Ruanui Nicholson
  • Anton Gulley
  • Jari Kaipio
  • Jennifer Eccles
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 28)

Abstract

Many parameter estimation problems are highly sensitive to errors. The Bayesian framework provides a methodology for incorporating these errors into our inversion. However, how to characterise the errors in a way that can be efficiently utilised remains a problem in many inversions. Recently the Bayesian approximation error method has been utilised as a systematic way of characterising errors that arise from inaccuracies in the model. We describe the Bayesian approximation error method and demonstrate its use in a homogenisation example. In this example, it is shown that the coarse scale homogenised parameter can be estimated by accounting for the significant modelling error using the Bayesian approximation error method. This modelling error arises from inverting using a model that does not account for the fine scale and has a coarse finite element discretisation.

Keywords

Bayesian inversion Modelling errors Homogenisation 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Ruanui Nicholson
    • 1
  • Anton Gulley
    • 1
  • Jari Kaipio
    • 1
  • Jennifer Eccles
    • 2
  1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand
  2. 2.School of EnvironmentThe University of AucklandAucklandNew Zealand

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