Correction: Minorization Condition and Convergence Rates for Markov Chain Monte Carlo

1995 ◽  
Vol 90 (431) ◽  
pp. 1136 ◽  
Author(s):  
Jeffrey Rosenthal
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Convergence Rates ◽  
Minorization Condition

scholarly journals On the convergence rates of some adaptive Markov chain Monte Carlo algorithms

2015 ◽  
Vol 52 (3) ◽  
pp. 811-825
Author(s):  
Yves Atchadé ◽  
Yizao Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Convergence Rates ◽  
Mixing Time ◽  
Regularity Conditions ◽  
Monte Carlo Algorithms ◽  
Mcmc Algorithms ◽  
Variation Distance ◽  
Importance Resampling

In this paper we study the mixing time of certain adaptive Markov chain Monte Carlo (MCMC) algorithms. Under some regularity conditions, we show that the convergence rate of importance resampling MCMC algorithms, measured in terms of the total variation distance, is O(n-1). By means of an example, we establish that, in general, this algorithm does not converge at a faster rate. We also study the interacting tempering algorithm, a simplified version of the equi-energy sampler, and establish that its mixing time is of order O(n-1/2).

scholarly journals On the convergence rates of some adaptive Markov chain Monte Carlo algorithms

2015 ◽  
Vol 52 (03) ◽  
pp. 811-825
Author(s):  
Yves Atchadé ◽  
Yizao Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Convergence Rates ◽  
Mixing Time ◽  
Regularity Conditions ◽  
Monte Carlo Algorithms ◽  
Mcmc Algorithms ◽  
Variation Distance ◽  
Importance Resampling

In this paper we study the mixing time of certain adaptive Markov chain Monte Carlo (MCMC) algorithms. Under some regularity conditions, we show that the convergence rate of importance resampling MCMC algorithms, measured in terms of the total variation distance, isO(n-1). By means of an example, we establish that, in general, this algorithm does not converge at a faster rate. We also study the interacting tempering algorithm, a simplified version of the equi-energy sampler, and establish that its mixing time is of orderO(n-1/2).

On Markov Chain Monte Carlo Acceleration

1994 ◽  
Author(s):  
Alan E. Gelfand ◽  
Sujit K. Sahu
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo
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