A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets
A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets
复制标题
使用小波连续监测非线性剖面的贝叶斯方法
DOI：
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发表时间：
2018
影响因子：
2.3
通讯作者：
Yun Yang
中科院分区：
文献类型：
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作者：
Roumen Varbanov;E. Chicken;A. Linero;Yun Yang
我们考虑函数观测序列中的变点检测和估计。当过程的质量以这种观察为特征时，通常会出现这种设置，称为配置文件，并且可以使用结构变化的监控配置文件来确保过程随着时间的推移的稳定性。虽然人们对第二阶段轮廓监测的兴趣有所增加，但很少有方法从贝叶斯的角度来处理这个问题。我们提出了一种基于小波的贝叶斯方法，该方法基于变化点的后验分布进行推断，而不对轮廓的形式施加限制性假设。通过得到这种后验分布的解析形式，我们允许所提出的方法在不使用马尔科夫链蒙特卡罗(MCMC)近似的情况下在线运行。小波是从受噪声污染的观测中估计非线性信号的有效工具，它使我们能够灵活地区分轮廓的持续变化和过程的内在变异性。我们在小波域中分析观测到的轮廓，并考虑对应于序列中未知变化的系数的两种可能的先验分布。这些先验，以前在非参数回归设置中应用，产生了超参数的自由调谐选择。我们介绍了随着时间的推移控制计算复杂性及其对性能影响的其他考虑因素。在仿真数据上，该方法的性能明显优于相关的频域竞争者。
We consider change‐point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet‐based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise‐contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning‐free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.