Abstract
Reliable inference of change points that are insensitive to deviations from model assumptions is essential in many real applications. We propose a two‐step iteration algorithm called detection‐pruning algorithm for multiple change point detection in the presence of outliers. In the two‐step iteration algorithm, first, a set of change points is efficiently detected based on a “cleaned” posterior; then, the outliers are explicitly pruned based on the set of change points simulated in the previous step. We use simulation and a real data analysis to demonstrate the effectiveness of the method and apply the method to the magnitude‐frequency distributions of deep earthquakes. We demonstrate the efficient detection of b ‐value change points and simultaneously the identification of a complete earthquake catalog with a time‐inhomogeneous completeness threshold for New Zealand deep earthquakes. Implications of the finding are also discussed.