用于完美采样算法的分层多移位耦合（CFTP入门）
Layered Multishift Coupling for use in Perfect Sampling Algorithms (with a primer on CFTP)
摘要：
在这篇文章中，我们描述了一个新的耦合技术，这是有用的各种完美的采样算法。多移位耦合器产生随机函数f（），使得对于每个实数x，f（x）-x由相同的固定概率分布（例如正态分布）控制。我们开发了一类分层多频移耦合器，它是简单的，有几个有用的性质。例如，对于标准正态分布，分层多移位耦合器生成f（），它（令人惊讶地）将长度为L的间隔映射到少于2+L/2.35个点-在对每个这样的图像点执行计算的应用中是有用的。分层多移位耦合器改进并简化了用于从若干分布生成完全随机样本的算法，所述若干分布包括自伽马分布、用于贝叶斯推断的后验分布以及用于某些存储系统的稳态分布。我们还使用分层多移位耦合器开发了一个基于马尔可夫链的完美抽样算法的自规范分布。应组织者的要求，我们首先介绍CFTP（来自过去的耦合）; CFTP和Fill算法是使用耦合马尔可夫链生成完美随机样本的两种主要技术。
英文摘要：
In this article we describe a new coupling technique which is useful in a variety of perfect sampling algorithms. A multishift coupler generates a random function f() so that for each real x, f(x)-x is governed by the same fixed probability distribution, such as a normal distribution. We develop the class of layered multishift couplers, which are simple and have several useful properties. For the standard normal distribution, for instance, the layered multishift coupler generates an f() which (surprisingly) maps an interval of length L to fewer than 2+L/2.35 points --- useful in applications which perform computations on each such image point. The layered multishift coupler improves and simplifies algorithms for generating perfectly random samples from several distributions, including the autogamma distribution, posterior distributions for Bayesian inference, and the steady state distribution for certain storage systems. We also use the layered multishift coupler to develop a Markov-chain based perfect sampling algorithm for the autonormal distribution. At the request of the organizers, we begin by giving a primer on CFTP (coupling from the past); CFTP and Fill's algorithm are the two predominant techniques for generating perfectly random samples using coupled Markov chains.
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