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A poisson process whose rate is a hidden Markov process
D. S. Freed, L. A. Shepp
Journal:

Advances in Applied Probability / Volume 14 / Issue 1 / March 1982

Published online by Cambridge University Press:

01 July 2016, pp. 21-36

Print publication:

March 1982
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Let a Poisson process be observed whose output rate is one of two levels given by the state of an unseen Markov process. If one of the levels is 0, a simple formula is given for the best guess of the state at any instant based on the stream of past Poisson events. In other cases bounds are given for the likelihood ratio of the state probabilities given the event stream.

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A poisson process whose rate is a hidden Markov process