74 citations · 142 across the 17 of their papers we have counts for
20 papers
Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems
Jan Blechschmidt, Oliver G. Ernst, Moritz Poguntke +1
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference - Markov chain Monte Carlo (MCMC) - is sequ…
Delayed Acceptance Slice Sampling
Kevin Bitterlich, Daniel Rudolf, Björn Sprungk
Slice sampling is a well-established Markov chain Monte Carlo method for approximate sampling of target distributions which are only known up to a normalizing constant. The method…
Weak Poincaré inequality comparisons for ideal and hybrid slice sampling
Sam Power, Daniel Rudolf, Björn Sprungk +1
Using the framework of weak Poincaré inequalities, we provide a general comparison between Hybrid and Ideal Slice Sampling in terms of their corresponding Dirichlet forms. In parti…
Metropolis-adjusted interacting particle sampling
Björn Sprungk, Simon Weissmann, Jakob Zech
In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samp…
Wasserstein convergence rates of increasingly concentrating probability measures
Mareike Hasenpflug, Daniel Rudolf, Björn Sprungk
For we consider the sequence of probability measures , where is determined by a density that is…
Robust random walk-like Metropolis-Hastings algorithms for concentrating posteriors
Daniel Rudolf, Björn Sprungk
Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly…
Dimension-independent Markov chain Monte Carlo on the sphere
H. C. Lie, D. Rudolf, B. Sprungk +1
We consider Bayesian analysis on high-dimensional spheres with angular central Gaussian priors. These priors model antipodally symmetric directional data, are easily defined in Hil…
Geometric convergence of elliptical slice sampling
Viacheslav Natarovskii, Daniel Rudolf, Björn Sprungk
For Bayesian learning, given likelihood function and Gaussian prior, the elliptical slice sampler, introduced by Murray, Adams and MacKay 2010, provides a tool for the construction…
The linear conditional expectation in Hilbert space
Ilja Klebanov, Björn Sprungk, T. J. Sullivan
The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important rôle in approximate Bayesia…
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Martin Eigel, Oliver Ernst, Björn Sprungk +1
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on…
Stability of doubly-intractable distributions
Michael Habeck, Daniel Rudolf, Björn Sprungk
Doubly-intractable distributions appear naturally as posterior distributions in Bayesian inference frameworks whenever the likelihood contains a normalizing function . Having tw…
Wasserstein sensitivity of Risk and Uncertainty Propagation
Oliver G. Ernst, Alois Pichler, Björn Sprungk
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a se…
On the Local Lipschitz Stability of Bayesian Inverse Problems
Björn Sprungk
In this note we consider the stability of posterior measures occuring in Bayesian inference w.r.t. perturbations of the prior measure and the log-likelihood function. This extends…
On Expansions and Nodes for Sparse Grid Collocation of Lognormal Elliptic PDEs
Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini
This work is a follow-up to our previous contribution ("Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PD…
Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling
Viacheslav Natarovskii, Daniel Rudolf, Björn Sprungk
We prove Wasserstein contraction of simple slice sampling for approximate sampling w.r.t. distributions with log-concave and rotational invariant Lebesgue densities. This yields, i…
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…
On a Metropolis-Hastings importance sampling estimator
Daniel Rudolf, Björn Sprungk
A classical approach for approximating expectations of functions w.r.t. partially known distributions is to compute the average of function values along a trajectory of a Metropoli…
Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)
Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini
We give a convergence proof for the approximation by sparse collocation of Hilbert-space-valued functions depending on countably many Gaussian random variables. Such functions appe…
Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems
Oliver G. Ernst, Björn Sprungk, Hans-Jörg Starkloff
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary pro…
On a generalization of the preconditioned Crank-Nicolson Metropolis algorithm
Daniel Rudolf, Björn Sprungk
Metropolis algorithms for approximate sampling of probability measures on infinite dimensional Hilbert spaces are considered and a generalization of the preconditioned Crank-Nicols…