Consistency of the posterior distribution in generalized linear inverse problems

@article{Bochkina2012ConsistencyOT,
  title={Consistency of the posterior distribution in generalized linear inverse problems},
  author={Natalia Bochkina},
  journal={Inverse Problems},
  year={2012},
  volume={29}
}
  • N. Bochkina
  • Published 14 November 2012
  • Mathematics
  • Inverse Problems
For ill-posed inverse problems, a regularized solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set of possible solutions, as other posterior estimates can be used as a solution to the inverse problem, such as the posterior mean which can be easier to compute in practice. In this paper we prove consistency of Bayesian solutions of an ill-posed linear inverse problem in the Ky Fan metric for a general class of likelihoods and… 
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