A Bayesian Online Change Point Model for Short Runs

Konstantinos Bourazas

Department of Economics, Athens University of Economics and Business

kbourazas@aueb.gr

                                            

 

                           

 

 Abstract

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In Statistical Process Control/Monitoring (SPC/M), our interest lies in detecting when a

process deteriorates from its "In Control" state, typically established through an extensive

Phase I exercise. Detecting shifts in multivariate short-horizon data for processes with

unknown parameters (i.e., without prior Phase I calibration) presents a significant challenge.

In this work, we propose a general self-starting Bayesian change point scheme, based on the

cumulative posterior probability that a change point has occurred. The methodology is

applicable to a wide range of distributions and types of shifts (e.g., location, scale), but we

focus on shifts in the mean of univariate or multivariate Normal distributions. The approach

extends the well-known Shiryaev's procedure by allowing both the process parameters and

the magnitude of shifts to be unknown, while relaxing several of the strict assumptions of

the classical formulation. Furthermore, posterior inference is provided for all model

parameters. The proposed scheme is illustrated using two real data sets, and its

performance is evaluated through a simulation study against standard alternatives.

 

Short bio

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Konstantinos Bourazas obtained his BSc in the Department of Mathematics of the University

of Patras in 2009 and his MSc and PhD in the Department of Statistics at the Athens

University of Economics and Business in 2014 and 2021 respectively. Furthermore, he was a

postdoctoral researcher at the KIOS Research and Innovation Center of Excellence,

University of Cyprus (2022-2024), at the Department of Statistical Sciences, Università

Cattolica del Sacro Cuore, Milan (2021-2022), and at the Department of Mathematics,

University of Ioannina (2021-2023). Currently, he is a postdoctoral researcher at the

Department of Economics, and a visiting professor in the Faculty of Political and Social

Sciences, Università Cattolica del Sacro Cuore, Milan.His research interests are in the areas of Statistical Process Control and Monitoring,

Bayesian Statistics, Change Point Models, Fraud Detection, Replication Studies, and

Applied Statistics. He won the Brumbaugh Award 2024 with Frédéric Sobas and Panagiotis

Tsiamyrtzis for the work “Predictive ratio CUSUM (PRC): A Bayesian approach in online

change point detection of short runs” as the publication with the largest single contribution

to the development of industrial application of quality control in 2023. His teaching

experience is mainly in Probability and Statistics, Data Analysis with R, and Data

Visualization with Tableau.