论文标题
SARD方法的半分离控制功能
Semi-Exact Control Functionals From Sard's Method
论文作者
论文摘要
考虑了后验预期量的利益量的数值近似。提出了一种新型的控制变量技术，用于基于Stein的方法和由于SAD而引起的数值整合方法的马尔可夫链蒙特卡洛输出的后处理。在高斯语境中，所得估计量在多个方面被证明是确切的，而经验结果表明，估计值近似于伯恩斯坦 - 冯·蒙斯限制的高斯群组方法。主要的理论结果在马尔可夫链不会留下后验不变的设置中建立了偏差校正属性。经过一系列贝叶斯推理任务呈现经验结果。本文中使用的所有方法均在R软件包ZVCV中使用。
The numerical approximation of posterior expected quantities of interest is considered. A novel control variate technique is proposed for post-processing of Markov chain Monte Carlo output, based both on Stein's method and an approach to numerical integration due to Sard. The resulting estimators are proven to be polynomially exact in the Gaussian context, while empirical results suggest 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 are presented across a selection of Bayesian inference tasks. All methods used in this paper are available in the R package ZVCV.
