Sequential change-point detection via the Cross-Entropy method

Change-point problems (or break point problems, disorder problems) can be considered one of the central issues of statistics, connecting asymptotic statistical theory and Monte Carlo methods, frequentist and Bayesian approaches, fixed and sequential procedures. In many real applications, observations are taken sequentially over time, or can be ordered with respect to some other criterion. The basic question, therefore, is whether the data obtained are generated by one or by many different probabilistic mechanisms. Change-point problems arise in a wide variety of fields, including biomedical signal processing, speech and image processing, climatology, industry (e.g. fault detection) and financial mathematics. In this paper, we apply the Cross-Entropy method to a sequential change-point problem. We obtain estimates for thresholds in the Shiryaev-Roberts procedure and the CUSUM procedure. We provide examples with generated sequences to illustrate the effectiveness of our approach to the problem.