Bayesian posterior contraction rates for linear severely ill-posed inverse problems

  title={Bayesian posterior contraction rates for linear severely ill-posed inverse problems},
  author={Sergios Agapiou and Andrew M. Stuart and Yuan-Xiang Zhang},
  journal={Journal of Inverse and Ill-posed Problems},
  pages={297 - 321}
Abstract. We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function. The observational noise is assumed to be Gaussian; as a consequence the prior is conjugate to the likelihood so that the posterior distribution is also Gaussian. We study Bayesian posterior consistency in the small observational noise limit. We… 

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