Three Examples of Monte-Carlo Markov Chains: At the Interface Between Statistical Computing, Computer Science, and Statistical Mechanics

1995 ◽  
pp. 43-56 ◽  
Author(s):  
Persi Diaconis ◽  
Susan Holmes
Keyword(s):  
Monte Carlo ◽  
Statistical Mechanics ◽  
Markov Chains ◽  
Computer Science ◽  
Statistical Computing

scholarly journals Concentration of measure and mixing for Markov chains

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Malwina Luczak
Keyword(s):  
Statistical Mechanics ◽  
Markov Chains ◽  
Computer Science ◽  
Stationary Distribution ◽  
Concentration Of Measure ◽  
Convergence To Equilibrium ◽  
Rapid Convergence ◽  
Strong Concentration ◽  
Local Dynamics ◽  
International Audience

International audience We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We illustrate our results with applications to some known chains from computer science and statistical mechanics.

scholarly journals A Bayesian model for binary Markov chains

2004 ◽  
Vol 2004 (8) ◽  
pp. 421-429 ◽  
Author(s):  
Souad Assoudou ◽  
Belkheir Essebbar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Bayesian Estimation ◽  
Bayesian Model ◽  
Transition Probabilities ◽  
Simulated Data ◽  
Bayesian Estimator ◽  
Jeffreys Prior ◽  
Data Set

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

scholarly journals Using systematic sampling selection for Monte Carlo solutions of Feynman-Kac equations

2008 ◽  
Vol 40 (2) ◽  
pp. 454-472 ◽  
Author(s):  
Ivan Gentil ◽  
Bruno Rémillard
Keyword(s):  
Monte Carlo ◽  
Markov Chains ◽  
Selection Method ◽  
Systematic Sampling ◽  
Selection Methods ◽  
Convergence Properties ◽  
Main Motivation ◽  
Empirical Basis ◽  
Convergence Results ◽  
Selection For

While the convergence properties of many sampling selection methods can be proven, there is one particular sampling selection method introduced in Baker (1987), closely related to ‘systematic sampling’ in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. We will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.

Markov Chains in Monte Carlo

1981 ◽  
Vol 54 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Hans Sagan
Keyword(s):  
Monte Carlo ◽  
Markov Chains
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