Andreas Hofinger and Hanna K Pikkarainen 2007 Inverse Problems 23 2469 doi:10.1088/0266-5611/23/6/012
Andreas Hofinger and Hanna K Pikkarainen
Show affiliationsRecently, the metrics of Ky Fan and Prokhorov were introduced as a tool for studying convergence of regularization methods for stochastic ill-posed problems. In this work, we show that the Bayesian approach to linear inverse problems can be examined in the new framework as well. We consider the finite-dimensional case where the measurements are disturbed by an additive normal noise, and the prior distribution is normal. Convergence and convergence rate results for the posterior distribution are obtained when the covariance matrices are proportional to the identity matrix.
02.50.Ng Distribution theory and Monte Carlo studies
65F22 Ill-posedness, regularization
60H25 Random operators and equations (See also 47B80)
Issue 6 (December 2007)
Received 14 November 2006, in final form 10 September 2007
Published 19 October 2007
Andreas Hofinger and Hanna K Pikkarainen 2007 Inverse Problems 23 2469
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