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Bayesian Approximation Error Approach

The Bayesian approximation error (BAE) approach belongs to the class of approximate Bayesian computation, with specific focus on inverse problems. The target is to carry out severe model reduction, to use approximate (physical) models and to neglect the estimation of various uninteresting (distributed) parameters. Inverse problems, by definition, do not tolerate the related errors (without feasible modelling of these). The key is to propagate the related errors to an additive error term and then formally marginalize over this vector-valued random variable. At this stage, a normal approximation for the likelihood distribution is usually adopted and point and spread (covariance) estimates are computed.

The approach has proven to work with different types of modelling errors and approximations such as severe model reduction, unknown boundary data (or operators), approximate physical models, marginalization over uninteresting distributed parameters, domain geometry and truncated decompositions of unknowns.


Past and present collaborators

  • Professor Erkki Somersalo, Case Western Reserve University, Department of Mathematics.

  • Professor Daniela Calvetti, Case Western Reserve University, Department of Mathematics.

  • Professor Heikki Haario, Lappeenranta University of Technology, Department of Mathematics.

  • Professor Simon Arridge, University College London.

Recent publications


A. Koulouri, V. Rimpilainen, M. Brookes, J.P. Kaipio
Compensation of domain modelling errors in the inverse source problem of the Poisson equation: Application in electroencephalographic imaging
Applied numerical mathematics, 106: 24-36, 2016.


M. Mozumder, T. Tarvainen, S. R. Arridge, J. P. Kaipio, C. D’Andrea and V. Kolehmainen
Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography
Inverse Problems and Imaging, 10(1): 227-246, 2016.


M. Mozumder, T. Tarvainen, J. P. Kaipio, S. R. Arridge and V. Kolehmainen
Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography
Journal of the Optical Society of America A 31(8):1847-1855, 2014.


A. Pulkkinen, V. Kolehmainen, J. P. Kaipio, B. T. Cox, S. R. Arridge and T. Tarvainen
Approximate marginalization of unknown scattering in quantitative photoacoustic tomography
Inverse Problems and Imaging 83: 811-829, 2014.


A. Lipponen, A. Seppänen, J.P. Kaipio
Electrical impedance tomography imaging with reduced-order model based on proper orthogonal decomposition
Journal of Electronic Imaging, 22: 023008, 2013.


V. Kolehmainen, T. Tarvainen, S. R. Arridge and J. P. Kaipio.
Marginalization of uninteresting distributed parameters in inverse problems – Application to diffuse optical tomography.
International Journal for Uncertainty Quantification, 1:1-17, 2011.


J. Kaipio, V. Kolehmainen
Approximate marginalization over modelling errors and uncertainties in inverse problems.
Bayesian Theory and Applications, eds. P. Damien, P. Dellaportas, N. Polson, D. Stephens, Oxford University Press, 2013

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