Convergence results for the Bayesian inversion theory


In this paper we derive convergence results for regularized solutions of linear inverse problems obtained by the Bayesian approach in the Ky Fan metric. We show that the convergence rate is order optimal in finite dimensional spaces. Moreover, we prove that order optimal rates can be obtained for weighted Bayesian solutions when the dimension goes to infinity.

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.