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A numerical method for computing interval distributions for an inhomogeneous Poisson point process modified by random

Adam J Peterson1

  • 1Leibniz Institute for Neurobiology, Brenneckestrasse 6, 39118, Magdeburg, Germany. adam.peterson@lin-magdeburg.de.

Biological Cybernetics
|March 20, 2021
PubMed
Summary

This study presents a numerical method to calculate event detection intervals for Poisson point processes with dead times. This approach aids in understanding dead-time effects on event detection in various scientific fields.

Keywords:
Inhomogeneous processInterval distributionNumerical methodPoisson point processRandom dead timeSimulation

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Area of Science:

  • Stochastic processes
  • Computational neuroscience
  • Signal processing

Background:

  • Inhomogeneous Poisson point processes model discrete events.
  • Detector dead times can cause missed events, complicating interval analysis.
  • Closed-form solutions for interval distributions are often intractable.

Purpose of the Study:

  • To develop a numerical method for computing interval distributions.
  • To analyze arbitrary inhomogeneous Poisson point processes with arbitrary dead times.
  • To understand the relationship between rate functions, interval distributions, and dead-time effects.

Main Methods:

  • Numerical computation of interval distributions.
  • Modeling of arbitrary dead-time distributions.
  • Simulation-based verification for various point processes.
  • Assumptions include finite observation windows and non-refractory initial states.

Main Results:

  • A method to numerically compute interval distributions for dead-time modified Poisson processes.
  • Successful verification of the method using simulations.
  • Demonstration of the method's applicability to arbitrary rate and dead-time functions.

Conclusions:

  • The developed method provides a way to analyze event detection intervals under dead-time conditions.
  • Useful for modeling neuronal spike trains and other stochastic event data.
  • Facilitates understanding of how dead times influence observed event patterns.