Estimation of Parameters in Shot-Noise- Driven Doubly Stochastic Poisson Processes Using the EM Algorithm

H. Mino

doi:10.1055/s-0038-1625397

Methods of Information in Medicine, Table of Contents

Methods Inf Med 2007; 46(02): 151-154
DOI: 10.1055/s-0038-1625397

Original Article

Schattauer GmbH

Estimation of Parameters in Shot-Noise- Driven Doubly Stochastic Poisson Processes Using the EM Algorithm

Modeling of Pre- and Postsynaptic Spike Trains

H. Mino

¹Department of Electrical and Computer Engineering, Kanto Gakuin University, Yokohama, Japan

› Author Affiliations

Abstract

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

Full Text

References

References
1. Brillinger DR. The identification of point process systems. Ann Prob 1975; 3: 909-929.
2. Willie JS. Measuring association of a time series and a point process. J Appl Prob 1982; 19: 597-608.
3. Willie JS. Covariation of atime series and apoint process. J Appl Prob 1982; 19: 609-618.
4. Rigas AG. Estimation of certain parameters of a stationary hybrid process involving a time series and a point process. Math Biosci 1996; 133: 197-218.
5. Snyder DL, Miller MI. Random Point Processes in Time and Space. Second Edition.New York: Springer-Verlag; 1991
6. Cox DR, Lewis PW. The Statistical Analysis of Series of Events. London: Methuen; 1966
7. Grandell J. Double Stochastic Poisson Processes, Lecture notes in mathematics, 529. Berlin: Springer-Verlag; 1976
8. Ogata Y, Akaike H, Katsura K. The Application of Linear Intensity Models to the Investigation of Causal Relations between a Point Process and Another Stochastic Process. Ann Inst Stat Math 1982; 34 PartB: 373-387.
9. McLachlan GJ, Krishnan T. The EM Algorithm and Extensions. New York: John Wiley & Sons; 1996
10. Mino H. Parameter Estimation of the Intensity Process of Self-Exciting Point Processes Using the EM Algorithm. IEEE Trans on Instrumentation and Measurement 2001; IM-50: 658-664.