158 citations · 251 across the 17 of their papers we have counts for
19 papers
Please, not \textit{another} note about Generalized Inverses
Philipp Wacker
We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.
Polarized consensus-based dynamics for optimization and sampling
Leon Bungert, Tim Roith, Philipp Wacker
In this paper we propose polarized consensus-based dynamics in order to make consensus-based optimization (CBO) and sampling (CBS) applicable for objective functions with several g…
Ensemble-based gradient inference for particle methods in optimization and sampling
Claudia Schillings, Claudia Totzeck, Philipp Wacker
We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of partic…
Maximum a posteriori estimators in are well-defined for diagonal Gaussian priors
Ilja Klebanov, Philipp Wacker
We prove that maximum a posteriori estimators are well-defined for diagonal Gaussian priors on under common assumptions on the potential . Further, we show connecti…
Nested sampling for physical scientists
Greg Ashton, Noam Bernstein, Johannes Buchner +20
We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey deve…
Continuous time limit of the stochastic ensemble Kalman inversion: Strong convergence analysis
Dirk Blömker, Claudia Schillings, Philipp Wacker +1
The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlyin…
Complete Deterministic Dynamics and Spectral Decomposition of the Linear Ensemble Kalman Inversion
Leon Bungert, Philipp Wacker
The ensemble Kalman inversion (EKI) for the solution of Bayesian inverse problems of type , with being an unknown parameter, a given datum, and $\vare…
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…
Nested Sampling And Likelihood Plateaus
Doris Schittenhelm, Philipp Wacker
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space by an integral over the unit line by employing a pus…
On the Convergence of the Laplace Approximation and Noise-Level-Robustness of Laplace-based Monte Carlo Methods for Bayesian Inverse Problems
Claudia Schillings, Björn Sprungk, Philipp Wacker
The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are int…
Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion
Dirk Blömker, Claudia Schillings, Philipp Wacker +1
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, an…
Wavelet-based priors accelerate maximum-a-posteriori optimization in Bayesian inverse problems
Philipp Wacker, Peter Knabner
Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for re…
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…
Bayesian model selection for linear regression
Miguel de Benito Delgado, Philipp Wacker
In this note we introduce linear regression with basis functions in order to apply Bayesian model selection. The goal is to incorporate Occam's razor as provided by Bayes analysis…
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…