Gibbs, A. L. (2000). Bounding the convergence time of the Gibbs sampler in Bayesian image restoration, Biometrika. To appear. Home/Search Document Details and Download
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Convergence in the Wasserstein Metric for Markov Chain Monte Carlo .. - Gibbs (1999) (Correct)
....for creating a precise, a priori bound on the required number of iterations is applied to a Gibbs sampler used in Bayesian image restoration where the individual pixels are values from a [0; 1] grey scale. This method also allows an improvement to the bound on the convergence time found in Gibbs [10] for a similar problem where the pixels are binary. This improvement is given in Section 6. 2 Convergence in the Wasserstein Metric We begin by presenting a general method for bounding the convergence time of a discrete time Markov chain fX t g in terms of the Wasserstein metric. This method is ....
....distance arises from its coupling characterisation d TV ( inf P (X 6= Y ) where the infimum is taken over random variables X and Y whose distributions are and respectively. For examples of this, see Aldous and Diaconis [2] Rosenthal [21] Luby, Randall and Sinclair [15] and Gibbs [10]. To the author s knowledge, this paper is the first application of convergence in the Wasserstein metric to Markov chain Monte Carlo algorithms. The Wasserstein metric was chosen for this application because of its coupling characterisation, Equation (2) Total variation 5 distance is not ....
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Gibbs, Alison L. (1998). Bounding convergence time of the Gibbs Sampler in Bayesian image restoration. University of Toronto, Department of Statistics, Technical Report number 9808.
Convergence in the Wasserstein Metric for Markov Chain Monte Carlo .. - Gibbs Self-citation (Gibbs) (Correct)
....precise, a priori bound on the required number of iterations is applied to a Gibbs sampler used in Bayesian image restoration where the individual pixels are values from a [0; 1] grey scale. The method presented in Section 2 also allows an improvement to the bound on the convergence time found in Gibbs (2000) for a similar image restoration problem where the pixels are binary. This improvement is given in Section 4. MCMC CONVERGENCE IN THE WASSERSTEIN METRIC 3 The results of Section 4 include a precise O(N log N) bound on the convergence time of the stochastic Ising model, where N is the number of ....
....distance arises from its coupling characterization TV ( inf Pr(X 6= Y ) where the infimum is taken over random variables X and Y whose distributions are and respectively. For examples of this, see Aldous and Diaconis (1987) Rosenthal (1995) Luby, Randall and Sinclair (1995) and Gibbs (2000). In this paper, we introduce the use of the Wasserstein metric to assessing convergence of Markov chain Monte Carlo algorithms. If , are two probability measures on the same space X , the Wasserstein metric is W ( inf E[d(X; Y ) 2.1) where the infimum is taken over all random variables ....
[Article contains additional citation context not shown here]
Gibbs, A. L. (2000). Bounding the convergence time of the Gibbs sampler in Bayesian image restoration, Biometrika. To appear.
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