We show that any application of the technique of unbiased simulation becomes perfect simulation when coalescence of the two coupled Markov chains can be practically assured in advance. This happens when a fixed number of iterations is high enough that the probability of needing any more to achieve coalescence is negligible; we suggest a value of $10^{-20}$. This finding enormously increases the range of problems for which perfect simulation, which exactly follows the target distribution, can be implemented. We design a new algorithm to make practical use of the high number of iterations by producing extra perfect sample points with little extra computational effort, at a cost of a small, controllable amount of serial correlation within sample sets of about 20 points. Different sample sets remain completely independent. The algorithm includes maximal coupling for continuous processes, to bring together chains that are already close. We illustrate the methodology on a simple, two-state Markov chain and on standard normal distributions up to 20 dimensions. Our technical formulation involves a nonzero probability, which can be made arbitrarily small, that a single perfect sample point may have its place taken by a "string" of many points which are assigned weights, each equal to $\pm 1$, that sum to~$1$. A point with a weight of $-1$ is a "hole", which is an object that can be cancelled by an equivalent point that has the same value but opposite weight $+1$.

翻译：我们证明，当两个耦合马尔可夫链的融合在实际中可提前确保时，无偏模拟技术的任何应用都将变为完美模拟。当固定迭代次数足够高以至于需要更多迭代才能实现融合的概率可忽略不计时（建议采用$10^{-20}$），这种情况便会发生。这一发现极大地扩展了可实施完美模拟（即精确遵循目标分布）的问题范围。我们设计了一种新算法，通过以少量可控的序列相关性为代价（在约20个点的样本集内），以极少的额外计算量生成额外的完美样本点，从而充分利用高迭代次数。不同样本集保持完全独立。该算法包含连续过程的最大耦合方法，以拉近已接近的链。我们通过简单的二态马尔可夫链和高达20维的标准正态分布演示了该方法的有效性。我们的技术框架引入了一个可任意小的非零概率：单个完美样本点可能被一串由加权点组成的"链"所替代，其中每个点被赋予权重$\pm 1$，权重之和为$1$。权重为$-1$的点称为"空穴"，这种对象可被具有相同值但相反权重$+1$的等效点所抵消。