Metropolis Methods, Gaussian Proposals and Antithetic Variables

By Peter J. Green, Xiao-liang Han. 1992

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Control functionals for Monte Carlo integration (2014, methodology): “, 2013), (b) stratified sampling and related techniques (Rubinstein and Kroese, 2011), (c) antithetic variables (Green and Han, 1992) and more generally (randomized) quasiMonte-Carlo (RQMC) sampling (Dick and Pillichshammer, 2010), (d) Rao–Blackwellization (Robert and Casella, 2004; Douc and Robert,”
Zero variance Markov chain Monte Carlo for Bayesian estimators (2010, background): “These modifications have been achieved in many different ways, for example by trying to induce negative correlation along the chain path ([6,21,13,41,12]); by trying to avoid random walk behavior via successive over-relaxation ([1,36,7]); by hybrid Monte Carlo ([16,35,10,18,27]); by exploiting non r”
Slice Sampling (2000, methodology): “This method is analysed and discussed by Barone and Frigessi (1990) and by Green and Han (1992), though these discussions fail in some respects to properly elucidate the true beneﬁts and limitations of overrelaxation (Neal 1998).”
Control variates for estimation based on reversible Markov chain Monte Carlo samplers (2012, methodology): “An early reference for variance reduction for Markov chain samplers is Green and Han (1992), who exploited an idea of Barone and Frigessi (1989) and constructed antithetic variables that may achieve variance reduction in simple settings but do not appear to be widely applicable.”
Spatial Statistics and Bayesian Computation (1993, background): “Almost all MCMC algorithms originate in statistical physics (for a recent review, see, for example, Sokal (1989) or Gidas (1992)), though there are some novel variations in the statistical literature, including Hastings (1970), Barone and Frigessi (1989), Besag and Clifford (1989, 1991), Clifford an”
Inference from Iterative Simulation Using Multiple Sequences (1992, methodology): “…the iterative simulation algorithm itself may have to be altered in order to speed convergence, for example, by reparameterizing (Hills and Smith, 1992), adding auxiliary variables (Besag and Green, 1993) or improving the jumping step in the generalized Metropolis algorithm (Green and Han, 1991).”
Optimal Hoeffding bounds for discrete reversible Markov chains (2004, background): “This result is well known [see, e.g., Green and Han (1992)], but our derivation contains some new elements and will allow us to introduce most of the notation needed for the sequel in a smooth way.”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, background): “General approaches to reduction 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…”