UC Irvine

Change point detection is a critical analysis in various scientific fields such as finance, medicine, and climatology. Despite the recent developments in methods and algorithms, it remains challenging in many problems. In this dissertation, we address and apply the detection of change points in two research problems. The first problem was motivated by identifying the epileptic seizure onset time using multi-channel EEG data and detecting abrupt changes in stocks that might characterize major events in the financial market. We propose a change point method using spectral principal component analysis on multivariate time series. By combining multiple time series and allowing for lead-lag relationships, our method achieves not only improved detectability but also more precise estimate of the locations of change points. In the second problem, the goal was to detect the exact time points at which a neuron fires using observed noisy calcium fluorescence recordings. We solve this problem by developing a time-varying $\ell_0$ penalized approach to jointly detect spikes using a dynamic change point detection algorithm and estimate firing rates using a Gaussian-boxcar smoother. Our simulated and real studies demonstrate that improved accuracy can be achieved by robustly integrating the evolving neural dynamics within and across recording sessions in a longitudinal setting.