4 papers · 1 filter
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…