论文标题
MCMC置信区间和偏见
MCMC Confidence Intervals and Biases
论文作者
论文摘要
J.S.的最新论文“无需CLT的MCMC的简单置信区间” Rosenthal仅使用Chebyshev的不等式而不是CLT显示了简单的MCMC置信区间的推导。该结果需要关于估计器偏差和差异如何随迭代$ n $增长的某些假设。特别是，偏见为$ o（1/\ sqrt {n}）$。这个假设似乎很温和。通常认为，估计器偏差为$ O（1/n）$，因此为$ o（1/\ sqrt {n}）$。但是，研究人员提出了有关如何验证这一假设的问题。确实，我们证明了这个假设可能并不总是存在。在本文中，我们试图简化和削弱前面提到的论文中的假设，以使没有CLT的MCMC置信区间更广泛地适用。
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.
