A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets: Wavelet-Based Bayesian Profile Monitoring
A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets: Wavelet-Based Bayesian Profile Monitoring
复制标题
使用小波连续监测非线性剖面的贝叶斯方法：基于小波的贝叶斯剖面监测
DOI：
10.1002/qre.2409
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发表时间：
2019
影响因子：
2.3
通讯作者：
Yang, Yun
中科院分区：
文献类型：
--
作者：
Varbanov, Roumen;Chicken, Eric;Linero, Antonio;Yang, Yun
我们考虑函数观测序列中的变点检测和估计。当过程的质量由这种观察（称为配置文件）表征时，通常会出现这种设置，并且可以使用结构变化的监测配置文件来确保过程随时间的稳定性。虽然在第二阶段配置文件监测的兴趣已经增长，很少有方法从贝叶斯的角度来解决这个问题。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，而不对曲线的形式进行限制性假设。通过获得这种后验分布的分析形式，我们允许所提出的方法在线运行，而不使用马尔可夫链蒙特卡罗（MCMC）近似。Wavelet是从噪声污染的观测值中估计非线性信号的有效工具，使我们能够灵活地区分剖面的持续变化和过程的固有变异性。我们在小波域中分析观察到的配置文件，并考虑两种可能的先验分布对应的未知变化的序列中的系数。这些先验，以前应用于非参数回归设置，产生无调整的超参数选择。我们提出了额外的考虑因素，随着时间的推移，控制计算复杂性及其对性能的影响。所提出的方法显着优于相关的频率竞争对手的模拟数据。
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.