  In this paper, we study the problem of multiple change-point detection for a
univariate sequence under the epidemic setting, where the behavior of the
sequence alternates between a common normal state and different epidemic
states. This is a non-trivial generalization of the classical (single) epidemic
change-point testing problem. To explicitly incorporate the alternating
structure of the problem, we propose a novel model selection based approach for
simultaneous inference on both change-points and alternating states. Using the
same spirit as profile likelihood, we develop a two-stage alternating pruned
dynamic programming algorithm, which conducts efficient and exact optimization
of the model selection criteria and has $O(n^2)$ as the worst case
computational cost. As demonstrated by extensive numerical experiments,
compared to classical general-purpose multiple change-point detection
procedures, the proposed method improves accuracy for both change-point
estimation and model parameter estimation. We further show promising
applications of the proposed algorithm to multiple testing with locally
clustered signals, and demonstrate its advantages over existing methods in
large scale multiple testing, in DNA copy number variation detection, and in
oceanographic study.
