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 to Sard. The resulting estimators of posterior expected quantities of interest are proven to be polynomially exact in the Gaussian context, while empirical results suggest that the estimators approximate a Gaussian cubature method near the Bernstein–von Mises limit. The main theoretical result establishes a bias-correction property in settings where the Markov chain does not leave the posterior invariant. Empirical results across a selection of Bayesian inference tasks are presented.

中文翻译：

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Sard方法的半精确控制泛函

总结 提出了一种新的控制变量技术，用于马尔可夫链蒙特卡罗输出的后处理，基于 Stein 方法和 Sard 的数值积分方法。所得到的后验期望感兴趣量的估计量被证明在高斯环境中是多项式精确的，而经验结果表明，估计量接近于 Bernstein-von Mises 极限附近的高斯容积法。主要的理论结果在马尔可夫链不留下后验不变量的情况下建立了偏差校正属性。介绍了一系列贝叶斯推理任务的经验结果。