Bayesian multiple changepoint detection with missing data and its application to the magnitude-frequency distributions

摘要

The detection of abrupt changes in an evolving pattern of time series in the presenceof missing data still poses a challenge to real applications.We formulate themultiple changepoint problem into a latent Markov model on a countably infinitestate space. For efficiency-enhancing,we propose a partially collapsed Gibbssampler for the inference of the joint posterior of the number of changepointsand their locations. Variants of Viterbi algorithms are suggested for obtainingthe MAP estimates of random changepoints in the presence of missing data,which provides better performances in these varying-dimensional problems.The method is generally applicable for multiple changepoint detection undera variety of missing data mechanism. The method is applied to a case studyof the magnitude-frequency distribution of the 2010 Darfield M7.1 earthquakesequence in New Zealand. We find out some unusual features of the seismicb-value in the Darfield earthquake sequence. It is noted that two changepointsare detected and in contrast to the background seismic b-value, relatively lowb-values in the early aftershock propagation period are identified. We suggestthat this might be a forewarning of potentially devastatingly strong aftershocks.The advance in the method of b-value changepoint detection will enhance ourunderstanding of earthquake occurrence and potentially lead to improved riskforecasting.