Estimating the Probability that a Function Observed with Noise Is Convex
Estimating the Probability that a Function Observed with Noise Is Convex
复制标题
估计带有噪声的函数为凸函数的概率
DOI：
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发表时间：
2017
影响因子：
2.1
通讯作者：
S. Henderson
中科院分区：
文献类型：
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作者：
Nanjing Jian;S. Henderson
考虑一个实值函数，它只能在欧几里得空间内的一组有限设计点处通过随机模拟噪声来观测。我们希望确定是否存在一个凸函数，它在设计点处经过真实函数值。我们开发了一种渐近一致的贝叶斯序贯抽样程序，用于估计这种情况为真的后验概率。在每次迭代中，使用蒙特卡罗模拟来估计后验概率。我们提供了三种方差缩减方法——测度变换、接受 - 拒绝和条件蒙特卡罗。数值实验表明应首选条件蒙特卡罗方法。
Consider a real-valued function that can only be observed with stochastic simulation noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function values at the design points. We develop an asymptotically consistent Bayesian sequential sampling procedure that estimates the posterior probability of this being true. In each iteration, the posterior probability is estimated using Monte Carlo simulation. We offer three variance reduction methods -- change of measure, acceptance-rejection, and conditional Monte Carlo. Numerical experiments suggest that the conditional Monte Carlo method should be preferred.