Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
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Nicole E. Radde
und
Jonas Offtermatt
Abstract.
We consider convergence of the posterior distribution in a Bayesian parameter estimation framework in the large sample size limit for structurally non-identified problems. These belong to the class of ill-posed problems, and the large sample theory is not applicable here. In particular, the influence of the prior distribution does not vanish in the large sample size limit. We review recent results in this area and present ideas inspired from the theory of ill-posed inverse problems that can be used towards a more general concept of posterior convergence for non-identified problems.
Funding source: German Research Foundation (DFG)
Award Identifier / Grant number: Cluster of Excellence in Simulation Technology (EXC 310)
Funding source: Ministry of Science, Research and Arts (MWK) Baden-Württemberg
Award Identifier / Grant number: program for junior professors
We thank Barbara Kaltenbacher from the University of Klagenfurt for her careful proof reading of the manuscript and many valid remarks on previous versions of this work.
© 2014 by Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
- Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
- A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation
Artikel in diesem Heft
- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
- Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
- A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation
