Bayesian Multiple Change Point Detection in the Presence of Outliers and Its Application to the Magnitude‐Frequency Distributions

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.