18 citations · 32 across the 6 of their papers we have counts for
6 papers
Goodness-of-fit testing for nonlinear inverse problems with random observations
Remo Kretschmann, Han Cheng Lie
This work is concerned with nonparametric goodness-of-fit testing in the context of nonlinear inverse problems with random observations. Bayesian posterior distributions based upon…
Maximum a posteriori testing in statistical inverse problems
Remo Kretschmann, Frank Werner
This paper is concerned with a Bayesian approach to testing hypotheses in statistical inverse problems. Based on the posterior distribution , we want to…
Optimal regularized hypothesis testing in statistical inverse problems
Remo Kretschmann, Daniel Wachsmuth, Frank Werner
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of int…
Are minimizers of the Onsager-Machlup functional strong posterior modes?
Remo Kretschmann
In this work we connect two notions: That of the nonparametric mode of a probability measure, defined by asymptotic small ball probabilities, and that of the Onsager-Machlup functi…
Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems
Tapio Helin, Remo Kretschmann
In this paper we study properties of the Laplace approximation of the posterior distribution arising in nonlinear Bayesian inverse problems. Our work is motivated by Schillings et…
Generalized modes in Bayesian inverse problems
Christian Clason, Tapio Helin, Remo Kretschmann +1
Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (mod…