158 citations · 251 across the 17 of their papers we have counts for
7 papers · 1 filter
The lion in the attic -- A resolution of the Borel--Kolmogorov paradox
Leon Bungert, Philipp Wacker
The Borel--Kolmogorov paradox of conditioning with respect to events of prior probability zero has fascinated students and researchers since its discovery more than 100 years ago.…
Pointwise defined version of conditional expectation with respect to a random variable
Philipp Wacker
It is often of interest to condition on a singular event given by a random variable, e.g. for a continuous random variable . Conditional measures with respect to this…
MAP estimators for nonparametric Bayesian inverse problems in Banach spaces
Philipp Wacker
In order to rigorously define maximum-a-posteriori estimators for nonparametric Bayesian inverse problems for general Banach space valued parameters, we derive and prove certain pr…
A strongly convergent numerical scheme from Ensemble Kalman inversion
Dirk Blömker, Claudia Schillings, Philipp Wacker
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differen…
Laplace's method in Bayesian inverse problems
Philipp Wacker
In a Bayesian inverse problem setting, the solution consists of a posterior measure obtained by combining prior belief, information about the forward operator, and noisy observatio…
Probabilistic Estimates of the Maximum Norm of Random Neumann Fourier Series
Dirk Blömker, Philipp Wacker, Thomas Wanner
We study the maximum norm behavior of -normalized random Fourier cosine series with a prescribed large wave number. Precise bounds of this type are an important technical tool…
Pattern size in Gaussian fields from spinodal decomposition
Luigi Amedeo Bianchi, Dirk Blömker, Philipp Wacker
We study the two-dimensional snake-like pattern that arises in phase separation of alloys described by spinodal decomposition in the Cahn-Hilliard model. These are somewhat univers…