Probability of error bounds for failure diagnosis and classification in hidden Markov models
Hadjicostis, Christoforos N.
SourceProceedings of the IEEE Conference on Decision and Control
Proceedings of the IEEE Conference on Decision and Control
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In this paper we consider a formulation of the failure diagnosis problem in stochastic systems as a maximum likelihood classification problem: a diagnoser observes the system under diagnosis online and determines which candidate model (e.g., a fault-free model or a faulty model) is more likely given the observations. We are interested in measuring a priori the diagnosis/ classification capability of the diagnoser by computing offline the probability that the diagnoser makes an incorrect decision (irrespective of the actual observation sequence) as a function of the observation step. We focus on hidden Markov models and compute an upper bound on this probability as a function of the length of the sequence observed. We also find necessary and sufficient conditions for this bound to decay to zero exponentially with the number of observations. © 2008 IEEE.
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