Robust empirical bayes analyses of event rates
Technometrics
Simulation and the Monte Carlo Method
Simulation and the Monte Carlo Method
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Comparison of methodologies to assess the convergence of Markov chain Monte Carlo methods
Computational Statistics & Data Analysis
Zero variance Markov chain Monte Carlo for Bayesian estimators
Statistics and Computing
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This paper develops an extension of the Riemann sum techniques of Philippe (J. Statist. Comput. Simul. 59: 295–314) in the setup of MCMC algorithms. It shows that these techniques apply equally well to the output of these algorithms, with similar speeds of convergence which improve upon the regular estimator. The restriction on the dimension associated with Riemann sums can furthermore be overcome by Rao–Blackwellization methods. This approach can also be used as a control variate technique in convergence assessment of MCMC algorithms, either by comparing the values of alternative versions of Riemann sums, which estimate the same quantity, or by using genuine control variate, that is, functions with known expectations, which are available in full generality for constants and scores.