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Error Bounds for Some Approximate Posterior Measures in Bayesian Inference

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Numerical Mathematics and Advanced Applications ENUMATH 2019

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 139))

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Abstract

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of approximate posteriors that arise from approximating the data misfit or forward model. We review some error bounds for random and deterministic approximate posteriors that arise when the approximate data misfits and approximate forward models are random.

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References

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Acknowledgements

The research of HCL has been partially funded by Deutsche Forschungsgemeinschaft (DFG)—SFB1294/1—318763901 and by Universität Potsdam. The work of TJS has been partially supported by the Freie Universität Berlin within the Excellence Initiative of the German Research Foundation (DFG). The authors thank an anonymous referee for their feedback.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Potsdam, Germany

    Han Cheng Lie

  2. Mathematics Institute and School of Engineering, The University of Warwick, Coventry, UK

    T. J. Sullivan

  3. Zuse-Institut Berlin, Berlin, Germany

    T. J. Sullivan

  4. School of Mathematics, University of Edinburgh, Edinburgh, UK

    Aretha Teckentrup

Authors
  1. Han Cheng Lie
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  2. T. J. Sullivan
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  3. Aretha Teckentrup
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Corresponding author

Correspondence to Han Cheng Lie .

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Editors and Affiliations

  1. DIAM, Delft University of Technology, Delft, The Netherlands

    Fred J. Vermolen

  2. DIAM, Delft University of Technology, Delft, The Netherlands

    Cornelis Vuik

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Lie, H.C., Sullivan, T.J., Teckentrup, A. (2021). Error Bounds for Some Approximate Posterior Measures in Bayesian Inference. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_26

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