Semi-exact control functionals from Sard’s method

Summary A novel control variate technique is proposed for the post-processing of Markov chain Monte Carlo output, based on both Stein’s method and an approach to numerical integration due Sard. The resulting estimators posterior expected quantities interest are proven be polynomially exact in Gaussian context, while empirical results suggest that approximate a cubature near Bernstein–von Mises limit. main theoretical result establishes bias-correction property settings where does not leave invariant. Empirical across selection Bayesian inference tasks presented.