Wavelet-Based Bayesian Approaches to Sequential Profile Monitoring

• Other Authors: Varbanov, Roumen (author)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Statistics
• Online Access: http://purl.flvc.org/fsu/fd/2018_Sp_Varbanov_fsu_0071E_14513

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, termed profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in profile monitoring has grown, few methods approach the problem from a Bayesian perspective. In this dissertation, we propose three wavelet-based Bayesian approaches to profile monitoring -- the last of which can be extended to a general process monitoring setting. First, we develop a general framework for the problem of interest in which we base inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. The proposed method uses an analytic form of the posterior distribution in order to run online without relying on Markov chain Monte Carlo (MCMC) simulation. Wavelets, an effective tool for estimating nonlinear signals from noise-contaminated observations, enable the method to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. Second, we modify the initial framework in a posterior approximation algorithm designed to utilize past information in a computationally efficient manner. We show that the approximation can detect changes of smaller magnitude better than traditional alternatives for curbing computational cost. Third, we introduce a monitoring scheme that allows an unchanged process to run infinitely long without a false alarm; the scheme maintains the ability to detect a change with probability one. We include theoretical results regarding these properties and illustrate the implementation of the scheme in the previously established framework. We demonstrate the efficacy of proposed methods on simulated data and significantly outperform a relevant frequentist competitor. === A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Spring Semester 2018. === April 20, 2018. === Includes bibliographical references. === Eric Chicken, Professor Co-Directing Dissertation; Antonio Linero, Professor Co-Directing Dissertation; Kevin Huffenberger, University Representative; Yun Yang, Committee Member.