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    This study introduces a Bayesian method to estimate the rate function of an inhomogeneous Poisson process (IHPP) observed with detector dead time. The approach improves signal inference accuracy for dead-time limited data.

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    Area of Science:

    • Statistics
    • Signal Processing
    • Optical Communications

    Background:

    • Estimating the rate function of an inhomogeneous Poisson process (IHPP) is crucial for applications like optical communications.
    • Detector limitations, specifically dead time, corrupt observed process data, complicating accurate rate function inference.
    • Existing methods struggle with inferring IHPP rates from dead-time affected observations.

    Purpose of the Study:

    • To develop a flexible nonparametric Bayesian method for inferring IHPP rate functions from dead-time limited data.
    • To assess the impact of dead time on IHPP rate function estimation.
    • To enhance the utility of sensor technology for signals with dead-time limitations.

    Main Methods:

    • A nonparametric Bayesian approach was proposed to infer the IHPP rate function.
    • The method specifically addresses challenges posed by dead-time limited process realizations.
    • Simulations were used to validate the inference approach's effectiveness.

    Main Results:

    • The proposed Bayesian method effectively infers IHPP rate functions from dead-time limited data.
    • Simulation results demonstrate the approach's accuracy and ability to overcome dead-time effects.
    • The method extends the applicability of existing sensor technologies for signal analysis.

    Conclusions:

    • The developed Bayesian inference approach offers a robust solution for estimating IHPP rate functions in the presence of dead time.
    • This technique significantly improves the accuracy of signal inference from corrupted observations.
    • The approach has practical utility in optical communications for channel modeling and validation.