Convergence assessment techniques for Markov chain Monte Carlo
Statistics and 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
Riemann sums for MCMC estimation and convergence monitoring
Statistics and Computing
Computational Statistics & Data Analysis
Estimating Bayes factors via thermodynamic integration and population MCMC
Computational Statistics & Data Analysis
Full wave form analysis for long-range 3D imaging laser radar
EURASIP Journal on Advances in Signal Processing - Special issue on advanced image processing for defense and security applications
A near-optimal algorithm for differentially-private principal components
The Journal of Machine Learning Research
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One major challenge with the modelization of complex problems using Markov chain Monte Carlo (MCMC) methods is the determination of the length of the chain in order to reach convergence. This paper is devoted to parametric empirical methods testing the stationarity. We compare the methods of Gelman and Rubin, Yu and Mykland, Raftery and Lewis, Geweke, Riemann sums and the subsampling. These methods are tested using three examples: the simple case of the generation of a normal random variable, a bivariate mixture of normal models and a practical case taken from hydrology, namely the shifting level model. Results show that no method works in every case. We therefore suggest a joint use of these techniques. The importance of determining carefully the burn-in period is also highlighted.