Print Email Facebook Twitter Bayesian Linear Inverse Problems in Regularity Scales with Discrete Observations Title Bayesian Linear Inverse Problems in Regularity Scales with Discrete Observations Author Yan, Dong (Student TU Delft) Gugushvili, Shota (Wageningen University & Research) van der Vaart, A.W. (TU Delft Statistics) Date 2024 Abstract We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration near the true function and the prior mass of functions with inferior Galerkin approximation. We apply the general result to non-conjugate series priors, showing that these priors give near optimal and adaptive recovery in some generality, Gaussian priors, and mixtures of Gaussian priors, where the latter are also shown to be near optimal and adaptive. Subject 35R3062G20Adaptive estimationFixed designGalerkinGaussian priorHilbert scaleInterpolationLinear inverse problemNonparametric Bayesian estimationPosterior contraction rateRandom series priorRegressionRegularity scale To reference this document use: http://resolver.tudelft.nl/uuid:dafbd1f9-d043-4b34-b0ed-a3a6461d5ee1 DOI https://doi.org/10.1007/s13171-024-00342-0 Embargo date 2024-09-07 ISSN 0976-836X Source Sankhya A Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2024 Dong Yan, Shota Gugushvili, A.W. van der Vaart Files file embargo until 2024-09-07