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Explicit error bounds for Markov chain Monte Carlo
Wir beweisen explizite, d.h., nicht-asymptotische Fehlerabschatzungen fur Markov-Ketten-Monte-Carlo-Methoden. Ziel ist es, den Erwartungswert einer Funktion f bzgl. eines Mases π zu berechnen.Expand
Perturbation theory for Markov chains via Wasserstein distance
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful andExpand
On the size of the largest empty box amidst a point set
We prove that the volume of the largest empty box is of asymptotic order $1/n$ for $n\to\infty$ and fixed dimension . Expand
Positivity of hit-and-run and related algorithms
We prove positivity of the Markov operators that correspond to the hit-and-run algorithm, random scan Gibbs sampler, slice sampler and Metropolis algorithm with positive proposal. In particular, theExpand
Explicit error bounds for lazy reversible Markov chain Monte Carlo
We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. Expand
Error bounds for computing the expectation by Markov chain Monte Carlo
  • Daniel Rudolf
  • Computer Science, Mathematics
  • Monte Carlo Methods Appl.
  • 12 June 2009
We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Expand
On a Generalization of the Preconditioned Crank–Nicolson Metropolis Algorithm
Metropolis algorithms for approximate sampling of probability measures on infinite dimensional Hilbert spaces are considered, and a generalization of the preconditioned Crank–Nicolson proposal is introduced. Expand
An Upper Bound of the Minimal Dispersion via Delta Covers
We prove that there is a point set, such that the largest volume of such a test set without any point is bounded above by \(\frac {\log \vert \varGamma _\delta \vert }{n} + \delta . Expand
Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can be measured by the discrepancy betweenExpand
Computation of Expectations by Markov Chain Monte Carlo Methods
Markov chain Monte Carlo (MCMC) methods are a very versatile and widely used tool to compute integrals and expectations. In this short survey we focus on error bounds, rules for choosing the burn in,Expand