On a likelihood approach for Monte Carlo integration
On a likelihood approach for Monte Carlo integration
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DOI：
10.1198/016214504000001664
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发表时间：
2004-12-01
影响因子：
3.7
通讯作者：
Tan, ZQ
中科院分区：
文献类型：
--
作者：
Tan, ZQ
使用估计方程是构造蒙特卡罗估计量的常用方法。最近，Kong等人提出了一种蒙特卡罗积分的公式作为统计模型，明确了哪些信息被忽略，哪些信息被保留。从模拟数据中，基线测量估计的最大似然，然后通过替代估计的测量，估计感兴趣的积分。对于两种不同的情况下，独立的观察模拟从多个分布，我们表明，这种似然方法实现了最低的渐近方差可能通过使用估计方程。在第一种情况下，估计了设计分布的归一化常数，并考虑了Meng和Wong的桥式抽样估计方程。在第二种情况下，归一化常数的值是已知的，从而对基线测量施加线性约束。本文考虑了Hesterberg的分层重要抽样估计、Vach和Guibas的多重重要抽样估计以及Owen和Zhou的控制变量法等估计方程。
The use of estimating equations has been a common approach for constructing Monte Carlo estimators. Recently, Kong et al. proposed a formulation of Monte Carlo integration as a statistical model, making explicit what information is ignored and what is retained about the baseline measure. From simulated data, the baseline measure is estimated by maximum likelihood, and then integrals of interest are estimated by substituting the estimated measure. For two different situations in which independent observations are simulated from multiple distributions, we show that this likelihood approach achieves the lowest asymptotic variance possible by using estimating equations. In the first situation, the normalizing constants of the design distributions are estimated, and Meng and Wong's bridge sampling estimating equation is considered. In the second situation, the values of the normalizing constants are known, thereby imposing linear constraints on the baseline measure. Estimating equations including Hesterberg's stratified importance sampling estimator, Veach and Guibas's multiple importance sampling estimator, and Owen and Zhou's method of control variates are considered.