Multiresolution and hybrid Bayesian algorithms for automatic detection of change points

Abstract

Two methods for detection of step changes in noise corrupted piecewise-constant univariate datasets are presented. The aim is to determine automatically the number and position of any discontinuities in the mean. This problem is commonly known as the change-point problem. The multiresolution method presented involves performing a discrete wavelet transform, shrinking the coefficients via soft thresholding, and then correlating across scales. Also Bayesian algorithms have long been available; they yield good results but they are impossible to apply in many cases due to huge computational complexity. The technique is compared with previously published hybrid Bayesian algorithms. It is essential in any technique that the probability of false detections is low while retaining a sufficiently high probability of detection for correct change points. To this end the Student's t-test is introduced as a final stage after both methods. This eliminates most, if not all, false detections while retaining most correct ones. Simulation results are presented for each algorithm demonstrating that good performance is obtained for datasets with different characteristics.