Online change detection of Markov chains with unknown post-change transition probabilities

ABSTRACT

In this paper, we investigate the performance of cumulative sum (CUSUM) stopping rules for the online detection of unknown change point in a time homogeneous Markov chain. Under the condition that the post-change transition probabilities are unknown, we proposed two CUSUM type schemes for the detection. The first scheme is based on the maximum likelihood estimates of the post-change transition probabilities. This scheme is limited by its computation burden, which is mitigated by another scheme based on the reference transition probabilities selected from a prior known region. We give the bounds of the mean delay time and the mean time between false alarms to illustrate the effectiveness of the proposed schemes. The results of the simulation also demonstrate the feasibility of the proposed schemes.

Keywords:

• Change point
• Likelihood ratio
• Markov chain
• Mean delay time
• Mean time between false alarms

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M02, 62F03, 62F05.

Additional information

Funding

This work is supported by the National Basic Research Program of China (973 Program) (2011CB808000) and the National Natural Science Foundation of China (No 11171216).