Researchers of time series cross-sectional data regularly face the change-point problem, which requires them to discern between significant parametric shifts that can be deemed structural changes and minor parametric shifts that must be considered noise. In this paper, we develop a general Bayesian method for change-point detection in high-dimensional data and present its application in the context of the fixed-effect model. Our proposed method, hidden Markov Bayesian bridge model, jointly estimates high-dimensional regime-specific parameters and hidden regime transitions in a unified way. We apply our method to Alvarez, Garrett, and Lange’s (1991, American Political Science Review 85, 539–556) study of the relationship between government partisanship and economic growth and Allee and Scalera’s (2012, International Organization 66, 243–276) study of membership effects in international organizations. In both applications, we found that the proposed method successfully identify substantively meaningful temporal heterogeneity in parameters of regression models.

The enormous economic loss caused by power quality problems (more than $ 150 billion per year in USA) makes power quality monitoring an important component in power grid. With highly connected fragile digital equipment and appliances, Smart Grid has more stringent timeliness and reliability requirements on power quality monitoring. In this work, we propose a change-point detection theory-based power quality monitoring scheme to detect the most detrimental power quality events, such as voltage sags, transients and swells in a quick and reliable manner. We first present a method for single-sensor detection scenario. Based on that, we extend the scheme to multi-sensor joint detection scheme which further enhances the detection performance. A group of conventional power quality monitoring schemes (i.e. Root-mean-square, Short-time Fourier transform, MUSIC, and MBQCUSUM) are compared with the proposed scheme. Experimental results assert the superior of the proposed scheme in terms of detection latency and robustness.

We consider the segmentation problem of Poisson and negative binomial (i.e.overdispersed Poisson) rate distributions. In segmentation, an important issueremains the choice of the number of segments. To this end, we propose a penalized-likelihood estimator where the penaltyfunction is constructed in a non-asymptotic context following the works of L. Birgé and P.Massart. The resulting estimator is proved to satisfy an oracle inequality. Theperformances of our criterion is assessed using simulated and real datasets in the RNA-seqdata analysis context.

The problem of detecting an abrupt change in the distribution of an arbitrary, sequentially observed, continuous-path stochastic process is considered and the optimality of the CUSUM test is established with respect to a modified version of Lorden's criterion. We apply this result to the case that a random drift emerges in a fractional Brownian motion and we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H+1/2.

Our aim is to estimate the joint distribution of a finite sequence of independent categorical variables. We consider the collection of partitions into dyadic intervals and the associated histograms, and we select from the data the best histogram by minimizing a penalized least-squares criterion. The choice of the collection of partitions is inspired from approximation results due to DeVore and Yu. Our estimator satisfies a nonasymptotic oracle-type inequality and adaptivity properties in the minimax sense. Moreover, its computational complexity is only linear in the length of the sequence. We also use that estimator during the preliminary stage of a hybrid procedure for detecting multiple change-points in the joint distribution of the sequence. That second procedure still satisfies adaptivity properties and can be implemented efficiently. We provide a simulation study and apply the hybrid procedure to the segmentation of a DNA sequence.