Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications to Image Restoration

@article{Gibbs1999ConvergenceIT,
  title={Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications to Image Restoration},
  author={A. Gibbs},
  journal={Stochastic Models},
  year={1999},
  volume={20},
  pages={473 - 492}
}
  • A. Gibbs
  • Published 1999
  • Mathematics, Computer Science
  • Stochastic Models
Abstract In this paper, we show how the time for convergence to stationarity of a Markov chain can be assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The Wasserstein metric may be more easily applied in some applications, particularly those on continuous state spaces. Bounds on convergence time are established by considering the number of iterations required to approximately couple two realizations of the Markov chain to within ε tolerance. The… Expand
26 Citations
Perfect Simulation for Image Restoration
Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances
Perturbation theory for Markov chains via Wasserstein distance
Convergence bound in total variation for an image restoration model
On the Well-posedness of Bayesian Inverse Problems
  • J. Latz
  • Mathematics, Computer Science
  • SIAM/ASA J. Uncertain. Quantification
  • 2020
...
1
2
3
...

References

SHOWING 1-10 OF 39 REFERENCES
Bounding the convergence time of the Gibbs sampler in Bayesian image restoration
Exact sampling with coupled Markov chains and applications to statistical mechanics
An interruptible algorithm for perfect sampling via Markov chains
Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
Markov Chains for Exploring Posterior Distributions
On the Statistical Analysis of Dirty Pictures
Exact sampling and approximate counting techniques
  • M. Huber
  • Mathematics, Computer Science
  • STOC '98
  • 1998
...
1
2
3
4
...