A Bound on the Rate of Convergence for the Discrete Gibbs Sampler

1995 ◽  
Vol 9 (2) ◽  
pp. 211-215 ◽  
Author(s):  
I. H. Dinwoodie
Keyword(s):  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Gibbs Sampler ◽  
Occupation Measure ◽  
Computable Bound

We give a computable bound on the rate of convergence of the occupation measure for the Gibbs sampler to the stationary distribution.

Stability and exponential convergence of continuous-time Markov chains

2003 ◽  
Vol 40 (04) ◽  
pp. 970-979 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Exponential Convergence ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
The Relationship

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

Local contractivity of the process of a player rating variation in the Elo model with one adversary

2015 ◽  
Vol 25 (5) ◽  
Author(s):  
Vadim A. Avdeev
Keyword(s):  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Infinite Series ◽  
Limit Distribution ◽  
Rating Model ◽  
Upper Estimate

AbstractWe study the process of variation of a player rating in an infinite series of games with the same adversary in the Elo rating model. This process is shown to have a stationary distribution, an upper estimate of the rate of convergence to which is established. In a previous paper by the author, the existence of a limit distribution was proved under more stringent assumptions on the parameters of a rating model.

A new look at the Moran dam

1993 ◽  
Vol 30 (2) ◽  
pp. 489-495 ◽  
Author(s):  
W. Stadje
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Boundary Crossing ◽  
Simple Boundary ◽  
Crossing Probabilities ◽  
Independent And Identically Distributed ◽  
New Look

For the original Moran dam with independent and identically distributed inputs a representation of the stationary distribution is given which readily provides a geometric rate of convergence to this distribution. For the integer-valued case the stationary distribution can be expressed in terms of simple boundary crossing probabilities for the underlying random walk.

Improving Stochastic Relaxation for Gussian Random Fields

1990 ◽  
Vol 4 (3) ◽  
pp. 369-389 ◽  
Author(s):  
Piero Barone ◽  
Arnolodo Frigessi
Keyword(s):  
Rate Of Convergence ◽  
Gibbs Sampler ◽  
Random Fields ◽  
Numerical Experiments ◽  
Gaussian Random Fields ◽  
Covariance Matrices ◽  
Suitable Choice ◽  
Stochastic Algorithms ◽  
Convergence Properties ◽  
Stochastic Relaxation

In this paper, we are concerned with the simulation of Gaussian random fields by means of iterative stochastic algorithms, which are compared in terms of rate of convergence. A parametrized class of algorithms, which includes stochastic relaxation (Gibbs sampler), is proposed and its convergence properties are established. A suitable choice for the parameter improves the rate of convergence with respect to stochastic relaxation for special classes of covariance matrices. Some examples and numerical experiments are given.

A new look at the Moran dam

1993 ◽  
Vol 30 (02) ◽  
pp. 489-495 ◽  
Author(s):  
W. Stadje
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Boundary Crossing ◽  
Simple Boundary ◽  
Crossing Probabilities ◽  
Independent And Identically Distributed ◽  
New Look

For the original Moran dam with independent and identically distributed inputs a representation of the stationary distribution is given which readily provides a geometric rate of convergence to this distribution. For the integer-valued case the stationary distribution can be expressed in terms of simple boundary crossing probabilities for the underlying random walk.

Stability and exponential convergence of continuous-time Markov chains

2003 ◽  
Vol 40 (4) ◽  
pp. 970-979 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Exponential Convergence ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
The Relationship

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

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