Stochastic simulation
Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Comparing sweep strategies for stochastic relaxation
Journal of Multivariate Analysis
On rates of convergence of stochastic relaxation for Gaussian and non-Gaussian distributions
Journal of Multivariate Analysis
Stationarity detection in the initial transient problem
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
A spectral method for confidence interval generation and run length control in simulations
Communications of the ACM - Special issue on simulation modeling and statistical computing
Quantitative convergence assessment for Markov chain Monte Carlo via cusums
Statistics and Computing
Looking at Markov samplers through cusum path plots: a simple diagnostic idea
Statistics and Computing
Stopping criterion for a simulation-based optimization method
Proceedings of the 30th conference on Winter simulation
On Bayesian analyses and finite mixtures for proportions
Statistics and Computing
Over-relaxation methods and coupled Markov chains for Monte Carlo simulation
Statistics and Computing
A Spectral Estimator of Arma Parameters from Thresholded Data
Statistics and Computing
MCMC Sampler Convergence Rates for Hierarchical Normal Linear Models: A Simulation Approach
Statistics and Computing
Bayesian analysis of the Logit model and comparison of two Metropolis-Hastings strategies
Computational Statistics & Data Analysis
Perfect simulation for Reed-Frost epidemic models
Statistics and Computing
Computational Statistics & Data Analysis
Bayesian regression mixtures of experts for geo-referenced data
Intelligent Data Analysis
Environmental Modelling & Software
Parts-based segmentation with overlapping part models using Markov chain Monte Carlo
Image and Vision Computing
Parallel and interacting Markov chain Monte Carlo algorithm
Mathematics and Computers in Simulation
Comparing stochastic volatility models through Monte Carlo simulations
Computational Statistics & Data Analysis
Comparison of methodologies to assess the convergence of Markov chain Monte Carlo methods
Computational Statistics & Data Analysis
Environmental Modelling & Software
Malformed frogs: Bayesian and random-effect model analyses
International Journal of Data Analysis Techniques and Strategies
A Dirichlet process mixture of generalized Dirichlet distributions for proportional data modeling
IEEE Transactions on Neural Networks
The computational complexity of estimating MCMC convergence time
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Efficient Monte Carlo simulation via the generalized splitting method
Statistics and Computing
Bayesian neural networks for prediction of protein secondary structure
ADMA'05 Proceedings of the First international conference on Advanced Data Mining and Applications
A near-optimal algorithm for differentially-private principal components
The Journal of Machine Learning Research
Location Prediction Based on a Sector Snapshot for Location-Based Services
Journal of Network and Systems Management
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MCMC methods have effectively revolutionised the field of Bayesian statistics over the past few years. Such methods provide invaluable tools to overcome problems with analytic intractability inherent in adopting the Bayesian approach to statistical modelling.However, any inference based upon MCMC output relies critically upon the assumption that the Markov chain being simulated has achieved a steady state or ’’converged‘‘. Many techniques have been developed for trying to determine whether or not a particular Markov chain has converged, and this paper aims to review these methods with an emphasis on the mathematics underpinning these techniques, in an attempt to summarise the current ’’state-of-play‘‘ for convergence assessment techniques and to motivate directions for future research in this area.