Title:
Maximum a posteriori estimators in l(p) are well-defined for diagonal Gaussian priors
Author(s):
Klebanov, Ilja; Wacker, Philipp
Year of publication:
2023
Available Date:
2023-06-02T10:07:24Z
Abstract:
We prove that maximum a posteriori estimators are well-defined for diagonal Gaussian priors ,u on tp under common assumptions on the potential F. Further, we show connections to the Onsager-Machlup functional and provide a corrected and strongly simplified proof in the Hilbert space case p= 2, previously established by Dashti et al (2013 Inverse Problems 29 095017); Kretschmann (2019 PhD Thesis). These corrections do not generalize to the setting 1 ? p < 8, which requires a novel convexification result for the difference between the Cameron-Martin norm and the p-norm.
Part of Identifier:
e-ISSN (online): 1361-6420
Keywords:
inverse problems
maximum a posteriori estimator
Onsager-Machlup functional
small ball probabilities
sequence spaces
Gaussian measures
DDC-Classification:
510 Mathematik
Publication Type:
Wissenschaftlicher Artikel
URL of the Original Publication:
DOI of the Original Publication:
Journaltitle:
Inverse Problems
Publisher:
IOP Publishing
Department/institution:
Mathematik und Informatik
Institut für Mathematik
Comments:
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
