A general purpose strategy is proposed to realize asymptotically the zero-variance importance sampling. The unknown integration constant can also be calculated simultaneously. This strategy can sample efficiently from multi-dimensional zero-variance importance function which is multi-modal by particular Markov Chain random walk. Sampling from this kind of distribution has been a challenge for a long time. Moreover, by using the probability density function reconstruction method, the unknown integration constant can be estimated. This feature is absent in traditional Markov Chain Monte Carlo method. Some multi-dimensional integrals are analyzed carefully. The results show this strategy is efficient.

提出了一种渐近实现零方差重要性抽样的通用策略。未知积分常数也可以同时计算。该策略可以从多维零方差重要性函数（通过特定的马尔可夫链随机游走多模态）有效地进行采样。长期以来，从这种分布中进行采样一直是一个挑战。此外，通过使用概率密度函数重构方法，可以估计未知积分常数。传统的马尔可夫链蒙特卡洛方法没有此功能。仔细分析了一些多维积分。结果表明该策略是有效的。