Bayesian quickest changepoint detection approach to partially observe Markov processes

Partially observed Markov processes or the so-called hidden Markov models constitute a class of stochastic processes that are very often used in a variety of practical problems. In this paper, we investigate the efficiency of the most popular quickest changepoint detection algorithms in hidden Markov models of the Bayesian approach.We compare the performance of the Shiryaev, Shiryaev-Roberts, and CUSUM procedures. The efficiency criterion is to minimize the average delay to detection subject to a constraint on the probability of false alarms. The Shiryaev procedure performs the best operating characteristics (as expected). The Shiryaev-Roberts procedure performs only slightly worse operating characteristics. The most popular in practice CUSUM procedure performs significantly worse than other procedures.