Summary
Objectives
: 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.
Keywords
Random point process - EM algorithm - computer simulation - fluctuation - neural spike
trains