Variance reduction in MCMC

By M. Antonietta, Tenconi Paolo, Bressanini Dario. 2003

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Control variates for estimation based on reversible Markov chain Monte Carlo samplers (2012, methodology): “U/: .34/ This methodology has been used extensively in the literature, including, among others, by Andradòttir et al. (1993), Mira et al. (2003), Stein et al. (2004), Meyn (2007) and Hammer and Tjelmeland (2008).”
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation (2016, background): “Later Mira, Tenconi, and Bressanini (2003) extended this approach to continuous state spaces, observing that the optimal choice of h ( θ ) is intimately associated with the solution of the Poisson equation h and proposing to solve this equation numerically.”
Norges Teknisk-naturvitenskapelige Universitet Control Variates for the Metropolis-hastings Algorithm Control Variates for the Metropolis-hastings Algorithm (methodology): “Mira et al. (2003) use the zero-variance principle introduced in the physics literature to construct another estimator˜f (x) that is the sum of the original estimator f (x) and an additional term with expectation zero.”
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, background): “Later Mira et al. (2003) extended the approach of Assaraf and Caﬀarel (1999) observing that the optimal choice of h ( θ ) is intimately associated with the solution of the Poisson equation h ( θ ) = E θ | y [ g ( θ )] − g ( θ ) and proposing to solve this equation numerically.”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, background): “Following Mira et al. (2013), it is possible to rearrange the terms on the right hand side of Eqn.”