Nonparametric Bayesian online change point detection using kernel density estimation with nonparametric hazard function

This paper aims to develop Bayesian online change point detection (BOCD), a parametric change point detection method, into a nonparametric method to be able to detect change points in a free-distribution time series. Instead of using predefined exponential family distribution for predictive probability, we use kernel density estimation in which two possible options have been proposed. The first is manual constant bandwidth selection. This option provides a fast computation of KDE as it can follow dynamic programming. Another option for the best performance is a nonparametric bandwidth estimator. For the goal of fully nonparametric change point detection, the predefined hazard function in the BOCD method is changed to be a nonparametric estimator. The performance of the proposed method is intensively evaluated with simulated data and compared with other traditional methods. It is found that nonparametric BOCD gives a better solution in all cases as a consequence of the adaptive property of KDE. Furthermore, the real-life application of the method with real data demonstrated its outstanding performance in detecting change points across diverse datasets. This success signifies a promising solution for expanding the potential of change point detection algorithms across a broader range of fields through the use of a nonparametric approach. Nevertheless, it requires a sufficient amount of data to form a precise predictive distribution curve to accurately detect change points.