title: Estimation of parameters in Shot-Noise-Driven Doubly Stochastic Poisson processes using the EM algorithm--modeling of pre- and postsynaptic spike trains.
abstract: OBJECTIVE
  To estimate the parameters, the impulse response (IR) functions of some linear time-invariant systems generating intensity processes, in Shot-Noise-Driven Doubly Stochastic Poisson Process (SND-DSPP) in which multivariate presynaptic spike trains and postsynaptic spike trains can be assumed to be modeled by the SND-DSPPs.
  
  
  METHODS
  An explicit formula for estimating the IR functions from observations of multivariate input processes of the linear systems and the corresponding counting process (output process) is derived utilizing the expectation maximization (EM) algorithm.
  
  
  RESULTS
  The validity of the estimation formula was verified through Monte Carlo simulations in which two presynaptic spike trains and one postsynaptic spike train were assumed to be observable. The IR functions estimated on the basis of the proposed identification method were close to the true IR functions.
  
  
  CONCLUSIONS
  The proposed method will play an important role in identifying the input-output relationship of pre- and postsynaptic neural spike trains in practical situations.
authors.affiliation: Department of Electrical and Computer Engineering, Kanto Gakuin University, 1-50-1 Mutsuura E., Kanazawa-ku, Yokohama 236-8501, Japan. mino@ieee.org
authors.forename: H
authors.initials: H
authors.lastname: Mino
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D016012:Poisson Distribution; D012815:Signal Processing, Computer-Assisted; D015398:Signal Transduction; D013269:Stochastic Processes; D013995:Time