Riemann sums for MCMC estimation and convergence monitoring

By Anne Philippe, Christian P. Robert. 2001

28 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “her evaluations of the function f, and is in this sense a widely-applicable post-processing scheme. 2.2 Control functionals The score statistic has previously been used as a control variate (see e.g. Philippe and Robert, 2001). More recently Mira et al. (2013) constructed score-based control variate”
Control variates for estimation based on reversible Markov chain Monte Carlo samplers (2012, methodology): “Also, Philippe and Robert (2001) investigated the use of Riemann sums as a variance reduction tool in MCMC algorithms.”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, methodology): “ of Monte Carlo error that have been proposed in the literature include antithetic variables (Green and Han, 1992), control variates and Rao-Blackwellisation (Robert and Casella, 2004), Riemann sums (Philippe and Robert, 2001) and a plethora of MCMC schemes that aim to improve mixing (e.g. Girolami ”
Zero variance Markov chain Monte Carlo for Bayesian estimators (2010, methodology): “zero mean random variables under the distribution of interest), the variable z can be monitored to test convergence along the lines suggested by [11] and [38], where the same control variate z = ∇ log π is used.”
Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms (2014, unknown): “…(Gelfand and Smith (1990), Robert and Casella (2004)), hybrid Monte Carlo (Duane et al. (1987), Fort et al. (2003)), use of Riemann sums (Philippe and Robert (2001)) or of auxiliary variables (Swendsen andWang (1987), Mira and Tierney (2002)), exploitation of non reversible Markov…”