A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms

By Randal Douc, Christian P. Robert. 2009

46 citations recorded by the source corpus.

Casella and Robert (1996) presented a general Rao--Blackwellisation principle for accept-reject and Metropolis-Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computing and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all Metropolis-Hastings~based estimators while keeping the computing cost under control. We establish a central limit theorems for the improved estimators and illustrate their performances on toy examples.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, background): “…and more generally (randomized) quasi- Monte-Carlo (RQMC) sampling (Dick and Pillichshammer, 2010), (d) Rao–Blackwellization (Robert and Casella, 2004; Douc and Robert, 2011; Ghosh and Clyde, 2011; Olsson and Ryden, 2011), (e) Riemann sums (Philippe, 1997), (f) control variates (Glasserman, 2004;…”
Bayesian forecasting in economics and finance: A modern review (2022, methodology): “, 2020); or the use of ex-post variance reduction methods (Craiu and Meng, 2005; Douc and Robert, 2011; Owen, 2017; Baker et al., 2019).”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, background): “…and methodology is still active and continually branching (Papaspiliopoulos et al. 2007; An-drieu and Roberts 2009; (cid:32)Latuszy´nski et al. 2011; Douc and Robert 2011), progressively incorporating the capacities of parallel processors and GPUs (Lee et al. 2009; Jacob et al. 2011; Strid 2010;…”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, background): “Indeed, in a complex and high-dimension model, the construction of the appropriate partition is a challenge in itself as we often have no prior idea where the modal areas are.”