THE SAMPLE SIZE REQUIRED IN IMPORTANCE SAMPLING
THE SAMPLE SIZE REQUIRED IN IMPORTANCE SAMPLING
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DOI：
10.1214/17-aap1326
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发表时间：
2018-04-01
影响因子：
1.8
通讯作者：
Diaconis, Persi
中科院分区：
文献类型：
--
作者：
Chatterjee, Sourav;Diaconis, Persi
重要性抽样的目的是使用从不同的概率测度中抽取的大小为n的随机样本来估计给定函数关于概率测度v的期望值。如果两个测度mu和v彼此之间几乎是奇异的，这在实践中经常发生，则精确估计所需的样本量很大。在这篇文章中，它表明，在一个相当一般的设置，一个样本的大小约为exp（D（v||对于重要抽样的精确估计，D（v））是必要和充分的，其中D（v|| mu）是p.与v的Kullback Leibler散度。特别是，所需的样本量在对数标度中表现出一种截止值。应用该理论得到了单参数指数族（吉布斯测度）重要抽样所需样本容量的一般公式。
The goal of importance sampling is to estimate the expected value of a given function with respect to a probability measure v using a random sample of size n drawn from a different probability measure If the two measures mu and v are nearly singular with respect to each other, which is often the case in practice, the sample size required for accurate estimation is large. In this article, it is shown that in a fairly general setting, a sample of size approximately exp(D(v || mu)) is necessary and sufficient for accurate estimation by importance sampling, where D(v || mu) is the Kullback Leibler divergence of p. from v. In particular, the required sample size exhibits a kind of cut-off in the logarithmic scale. The theory is applied to obtain a general formula for the sample size required in importance sampling for one -parameter exponential families (Gibbs measures).