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Neural Computation

August 2010, Vol. 22, No. 8, Pages 1993-2001
(doi: 10.1162/neco.2010.07-09-1047)
© 2010 Massachusetts Institute of Technology
Estimating a State-Space Model from Point Process Observations: A Note on Convergence
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Physiological signals such as neural spikes and heartbeats are discrete events in time, driven by continuous underlying systems. A recently introduced data-driven model to analyze such a system is a state-space model with point process observations, parameters of which and the underlying state sequence are simultaneously identified in a maximum likelihood setting using the expectation-maximization (EM) algorithm. In this note, we observe some simple convergence properties of such a setting, previously un-noticed. Simulations show that the likelihood is unimodal in the unknown parameters, and hence the EM iterations are always able to find the globally optimal solution.