Comparative analysis of Bayesian and maximum likelihood estimators in change point problems with Poisson process

Abstract

Abstract Nowadays the application of change point analysis has been indispensable in a widerange of areas such as quality control, nance, environmetrics, medicine, geographics,and engineering. Identi cation of times where process changes would help minimizethe consequences that might happen afterwards. The main objective of this paper isto compare the change-point detection capabilities of Bayesian estimate and maxi-mum likelihood estimate. We applied Bayesian and maximum likelihood techniques toformulate change points having a step change and multiple number of change pointsin a Poisson rate. After a signal from c-chart and Poisson cumulative sum controlcharts have been detected, Monte Carlo simulation has been applied to investigate theperformance of Bayesian and maximum likelihood estimation. Change point detectioncapacities of Bayesian and maximum likelihood estimation techniques have been inves-tigated through simulation. It has been found that the Bayesian estimates outperformsstandard control charts well specially when there exists a small to medium size of stepchange. Moreover, it performs convincingly well in comparison with the maximum like-lihood estimator and remains good choice specially in con dence interval statisticalinference.Keywords: Bayesian estimate, change point, control chart, maximum likelihood esti-mate, Monte Carlo simulation.