延迟接受核的方差界
Variance bounding of delayed-acceptance kernels
摘要：
一个延迟接受版本的大都市-黑斯廷斯算法可以是有用的贝叶斯推理时，它是计算昂贵的计算真正的后验，但计算便宜的近似是可用的;延迟接受内核的目标相同的后验作为其相关的“父”大都市-黑斯廷斯内核。虽然链的任何泛函的遍历平均值的渐近方差不能小于，使用它的父母，每次迭代的平均计算时间可以小得多，所以对于一个给定的计算预算的延迟接受内核可以更有效。当链的所有$L^2$泛函的遍历平均的渐近方差是有限的时，称核是方差有界的。最近已经注意到，延迟接受核不需要方差边界，即使它的父核是。我们提供了继承的充分条件：对于非局部算法，如独立采样器，近似值的对数密度和真实值之间的差异应该是有界的;对于局部算法，提供了两组可供选择的条件。作为我们的初始产品，一般的结果，我们还提供充分条件对任何一对的建议，这样，对于任何共享的目标分布，如果一个大都市，黑斯廷斯内核使用的建议之一是方差边界，那么是大都市，黑斯廷斯内核使用其他建议。
英文摘要：
A delayed-acceptance version of a Metropolis--Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to calculate the true posterior, but a computationally cheap approximation is available; the delayed-acceptance kernel targets the same posterior as its associated "parent" Metropolis-Hastings kernel. Although the asymptotic variance of the ergodic average of any functional of the chain cannot be less than that obtained using its parent, the average computational time per iteration can be much smaller and so for a given computational budget the delayed-acceptance kernel can be more efficient. When the asymptotic variance of the ergodic averages of all $L^2$ functionals of the chain is finite, the kernel is said to be variance bounding. It has recently been noted that a delayed-acceptance kernel need not be variance bounding even when its parent is. We provide sufficient conditions for inheritance: for non-local algorithms, such as the independence sampler, the discrepancy between the log density of the approximation and that of the truth should be bounded; for local algorithms, two alternative sets of conditions are provided. As a by-product of our initial, general result we also supply sufficient conditions on any pair of proposals such that, for any shared target distribution, if a Metropolis-Hastings kernel using one of the proposals is variance bounding then so is the Metropolis-Hastings kernel using the other proposal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
