現今由於科技與網際網路的蓬勃發展，有關資料流分析的文章也越來越多，而變構點的偵測是分析資料流的一重要問題。在此篇論文裡，提供在貝氏觀念下，如何偵測出是否有變構點的方法。整個方法主要想法是當加入新資料後，檢定模型系數的後驗分配是否改變。整個過程包含三步驟，第一步，用Metroplois-Hastings 演算法產生後驗分配的樣本。第二步，把多維度資料映射到一維空間上。最後一步則是用兩樣本貝氏無母數適合度檢定檢驗後驗分配是否改變。接著由模擬方法驗證此方法的可行性。再將方法應用在網路新聞資料上，發現此筆資料的模型每十二個禮拜模型皆會改變。

Data Streams have become popular due to the burgeoning development of data collection devices. Detecting model changes is one of major difficulties in analyzing streaming data. In this thesis, we provide a procedure to detect model changes in the Bayesian perspective. The idea is to examine whether the posterior distributions of the past data and the current data are identical. The detection procedure consists of three steps. In the first step, we utilize the Metropolis-Hastings algorithm to draw samples from the two posterior distributions. In the second step, we map multi-dimensional posterior samples to one-dimensional samples. Last, we apply two- (one-dimensional) sample Bayesian nonparametric goodness-of-fit test to examine whether the model changes. Simulation studies showed the result of this procedure. Then, we applied the procedure to an online news popularity data and our conclusion supported the conjecture “model changes over time frequently”.

References
Al Labadi, L., Masuadi, E., and Zarepour, M. (2014). Two-sample bayesian nonparametric
goodness-of-fit test.
Bondesson, L. (1982). On simulation from infinitely divisible distributions. Advances in
Applied Probability, 14(04):855–869.
Ferguson, T. S. (1973). A bayesian analysis of some nonparametric problems. The annals of
statistics, pages 209–230.
Ferguson, T. S. and Klass, M. J. (1972). A representation of independent increment processes
without gaussian components. The Annals of Mathematical Statistics, 43(5):1634–1643.
Fernandes, K., Vinagre, P., and Cortez, P. (2015). A proactive intelligent decision support
system for predicting the popularity of online news. In Portuguese Conference on Artificial
Intelligence, pages 535–546. Springer.
Gama, J., Žliobaitė, I., Bifet, A., Pechenizkiy, M., and Bouchachia, A. (2014). A survey on
concept drift adaptation. ACM Computing Surveys (CSUR), 46(4):44.
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2014). Bayesian data analysis,
volume 2. Chapman & Hall/CRC Boca Raton, FL, USA.
Gurevich, G. and Vexler, A. (2005). Change point problems in the model of logistic regression.
Journal of Statistical Planning and Inference, 131(2):313–331.
Jordan, M. I. et al. (1995). Why the logistic function? a tutorial discussion on probabilities
and neural networks.
Kim, H.-J. and Siegmund, D. (1989). The likelihood ratio test for a change-point in simple
linear regression. Biometrika, pages 409–423.
Martin, A. D., Quinn, K. M., and Park, J. H. (2005). Markov chain monte carlo (mcmc)
package. URL (consulted Oct. 2006): http://mcmcpack. wustl. edu.
O’brien, S. M. and Dunson, D. B. (2004). Bayesian multivariate logistic regression. Biometrics,
60(3):739–746.
Quandt, R. E. (1958). The estimation of the parameters of a linear regression system obeying
two separate regimes. Journal of the american statistical association, 53(284):873–880.
Sethuraman, J. (1994). A constructive definition of dirichlet priors. Statistica sinica, pages
639–650.
Ulm, K. (1991). A statistical method for assessing a threshold in epidemiological studies.
Statistics in medicine, 10(3):341–349.
Zarepour, M. and Al Labadi, L. (2012). On a rapid simulation of the dirichlet process. Statistics
& Probability Letters, 82(5):916–924.