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

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.