Extension of Fill's perfect rejection sampling algorithm to general chains

Designing Perfect Simulation Algorithms using Local Correctness

Consider a randomized algorithm that draws samples exactly from a distribution using recursion. Such an algorithm is called a perfect simulation, and here a variety of methods for building this type of algorithm are shown to derive from the same result: the Fundamental Theorem of Perfect Simulation (FTPS). The FTPS gives two necessary and sufficient conditions for the output of a recursive probabilistic algorithm to come exactly from the desired distribution. First, the algorithm must terminate with probability 1. Second, the algorithm must be locally correct, which means that if the recursive…

部分拒绝采样基础

Fundamentals of Partial Rejection Sampling

本文介绍部分拒绝采样算法的基础，说明其通过仅重采样出错变量子集提升效率的特点，关联Lovász局部引理算法并给出自包含的算法形式与分析。

The Fundamental Theorem of Perfect Simulation

Here several perfect simulation algorithms are brought under a single framework, and shown to derive from the same probabilistic result, called here the Fundamental Theorem of Perfect Simulation (FTPS). An exact simulation algorithm has output according to an input distribution $π$. Perfect simulations are a subclass of exact simulations where recursion is used either explicitly or implicitly. The FTPS gives two simple criteria that, when satisfied, give a correct perfect simulation algorithm. First the algorithm must terminate in finite time with probability 1. Second, the algorithm must be l…

Exact Sampling from Perfect Matchings of Dense Nearly Regular Bipartite Graphs

We present the first algorithm for generating random variates exactly uniformly from the set of perfect matchings of a bipartite graph with a polynomial expected running time over a nontrivial set of graphs. Previous Markov chain approaches obtain approximately uniform variates for arbitrary graphs in polynomial time, but their general running time is $Θ(n^{26} (\ln n)^2).$ Our algorithm employs acceptance/rejection together with a new upper limit on the permanent of a form similar to Bregman's Theorem. For a graph with $2n$ nodes where the degree of every node is nearly $γn$ for a constant $γ…

Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author,two Markov chain Monte Carlo perfect sampling algorithms -- one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling -- are compared using as a case study the move-to-front (MTF) self-organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user-chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial sta…

马尔可夫负载均衡排队网络在平衡状态下的完美模拟

Perfect simulation of Markovian load balancing queueing networks in equilibrium

本文针对马尔可夫负载均衡排队网络平衡态模拟问题，提出三种基于支配过程和预序耦合的完美模拟算法，解决了状态空间无限且不变分布未知情况下的蒙特卡洛估计难题。

Layered Multishift Coupling for use in Perfect Sampling Algorithms (with a primer on CFTP)

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 w…