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## Nonparametric Bayesian approach to the detection of change point in statistical process control

#### Issah N. Suleiman [1] , M. Akif Bakır [2]

This paper gives an intensive overview of nonparametric Bayesian model relevant to the determination of change point in a process control. We first introduce statistical process control and develop on it describing Bayesian parametric methods followed by the nonparametric Bayesian modeling based on Dirichlet process. This research proposes a new nonparametric Bayesian change point detection approach which in contrast to the Markov approach of Chib [6] uses the Dirichlet process prior to allow an integrative transition of probability from the posterior distribution. Although the Bayesian nonparametric technique on the mixture does not serve as an automated tool for the selection of the number of components in the finite mixture. The Bayesian nonparametric mixture shows a misspecication model properly which has been explained further in the methodology. This research shows the principal step-bystep algorithm using nonparametric Bayesian technique with the Dirichlet process prior defined on the distribution to the detection of change point. This approach can be further extended in the multi-variate change point detection which will be studied in the near future.
Nonparametric, Bayesian, Change point, Clustering, Mixture model, Dirichlet process
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Birincil Dil en Matematik İstatistik Yazar: Issah N. Suleiman (Sorumlu Yazar) Yazar: M. Akif Bakır Yayımlanma Tarihi : 1 Haziran 2017
 Bibtex @araştırma makalesi { hujms451024, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2017}, volume = {46}, pages = {525 - 545}, doi = {}, title = {Nonparametric Bayesian approach to the detection of change point in statistical process control}, key = {cite}, author = {Suleiman, Issah N. and Bakır, M. Akif} } APA Suleiman, I , Bakır, M . (2017). Nonparametric Bayesian approach to the detection of change point in statistical process control. Hacettepe Journal of Mathematics and Statistics , 46 (3) , 525-545 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/38758/451024 MLA Suleiman, I , Bakır, M . "Nonparametric Bayesian approach to the detection of change point in statistical process control". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 525-545 Chicago Suleiman, I , Bakır, M . "Nonparametric Bayesian approach to the detection of change point in statistical process control". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 525-545 RIS TY - JOUR T1 - Nonparametric Bayesian approach to the detection of change point in statistical process control AU - Issah N. Suleiman , M. Akif Bakır Y1 - 2017 PY - 2017 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 525 EP - 545 VL - 46 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Nonparametric Bayesian approach to the detection of change point in statistical process control %A Issah N. Suleiman , M. Akif Bakır %T Nonparametric Bayesian approach to the detection of change point in statistical process control %D 2017 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 46 %N 3 %R %U ISNAD Suleiman, Issah N. , Bakır, M. Akif . "Nonparametric Bayesian approach to the detection of change point in statistical process control". Hacettepe Journal of Mathematics and Statistics 46 / 3 (Haziran 2017): 525-545 . AMA Suleiman I , Bakır M . Nonparametric Bayesian approach to the detection of change point in statistical process control. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 525-545. Vancouver Suleiman I , Bakır M . Nonparametric Bayesian approach to the detection of change point in statistical process control. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 545-525.