MCMC 互信互信和分裂 (MCMC Confidence Intervals and Biases)

The recent paper "Simple confidence intervals for MCMC without CLTs" by J.S. Rosenthal, showed the derivation of a simple MCMC confidence interval using only Chebyshev's inequality, not CLT. That result required certain assumptions about how the estimator bias and variance grow with the number of iterations $n$. In particular, the bias is $o(1/\sqrt{n})$. This assumption seemed mild. It is generally believed that the estimator bias will be $O(1/n)$ and hence $o(1/\sqrt{n})$. However, questions were raised by researchers about how to verify this assumption. Indeed, we show that this assumption might not always hold. In this paper, we seek to simplify and weaken the assumptions in the previously mentioned paper, to make MCMC confidence intervals without CLTs more widely applicable.

翻译：由J.S. Rosenthal最近发表的题为“没有CLT的MCMC的简单信任间隔”的论文罗森塔尔展示了一个简单的MCMC信任间隔,仅使用Chebyshev的不平等,而不是CLT。这一结果要求对估计偏差和差异与迭代数量的增加如何产生某些假设。特别是,偏差为$o(1/\sqrt{n})美元。这一假设似乎比较温和。人们普遍认为,估计偏差是O(1/n)美元,因此是$(1/\sqrt{n})美元。然而,研究人员提出了如何核实这一假设的问题。事实上,我们表明这一假设不一定能维持下去。在本文中,我们力求简化和削弱前述文件中的假设,使MC信任间隔不广泛适用CLTs。