The normal law under linear restrictions: simulation and estimation via minimax tilting
The normal law under linear restrictions: simulation and estimation via minimax tilting
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DOI：
10.1111/rssb.12162
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发表时间：
2017-01-01
影响因子：
5.8
通讯作者：
Botev, Z. I.
中科院分区：
文献类型：
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作者：
Botev, Z. I.
从高维截断多元正态分布的模拟是统计计算中经常出现的问题，并且通常仅通过使用近似马尔可夫链蒙特卡罗抽样才是可行的。本文提出了一种极小极大倾斜方法，用于截断多元正态分布下独立同分布数据的精确模拟。新的方法提供了一种模拟方法和一个有效的估计到目前为止棘手的高斯积分。证明了该估计量具有罕见的零相对误差渐近性质。数值实验表明，该计划提出的是准确的，在广泛的设置，竞争的估计方案失败。我们给出了一个应用程序，以准确的独立和同分布的数据模拟从概率回归模型的贝叶斯后验。
Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing and is typically only feasible by using approximate Markov chain Monte Carlo sampling. We propose a minimax tilting method for exact independently and identically distributed data simulation from the truncated multivariate normal distribution. The new methodology provides both a method for simulation and an efficient estimator to hitherto intractable Gaussian integrals. We prove that the estimator has a rare vanishing relative error asymptotic property. Numerical experiments suggest that the scheme proposed is accurate in a wide range of set-ups for which competing estimation schemes fail. We give an application to exact independently and identically distributed data simulation from the Bayesian posterior of the probit regression model.