Efficiency of Multivariate Control Variates in Monte Carlo Simulation

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Control functionals for Monte Carlo integration (2014, background): “Then a surrogate function f̃ =f −a1s1 −: : :−amsm is constructed such thatμ.f̃ /=μ.f/ and, for suitably chosen a1, : : : , am ∈R, a variance reduction σ2.f̃ /<σ2.f/ is obtained (see for example Rubinstein and Marcus (1985)).”
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation (2016, background): “It can be shown (Rubinstein and Marcus 1985) that this choice of polynomial coefficients φ = φ ∗ is characterized as the minimizer of the variance ratio and at this minimum so that greater variance reduction is expected in the case where a linear combination of the elements of the vector u ( θ ) is…”
Convergence rates for a class of estimators based on Stein’s method (2016, background): “is constructed such that automatically ∫ f ′ d = ∫ f d and, for suitably chosen {ai}i=1, a variance reduction σ 2(f ′) < σ 2(f ) might be obtained; for further details see, for example, [39].”
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, background): “Other attempts to address Type II intractability include the popular approximation scheme of Rue et al. (2009) and the references therein.”