Quantifying statistical interdependence, part III: N > 2 point processes

Area of Science:

• Computational neuroscience
• Time series analysis
• Statistical modeling

Background:

• Stochastic Event Synchrony (SES) is a similarity measure for time series based on event alignment.
• Previous work developed SES for pairwise (1D and multi-D) point processes.
• Extending SES to N > 2 signals is crucial for analyzing complex systems.

Purpose of the Study:

• To extend Stochastic Event Synchrony (SES) to analyze synchrony across N > 2 time series.
• To develop a robust statistical inference framework for N-variate SES.
• To evaluate the performance of N-variate SES on synthetic and real-world neuroscience data.

Main Methods:

• Developed an N-variate SES framework using statistical inference with alternating steps for parameter estimation and alignment refinement.
• Employed maximum a posteriori (MAP) estimation for SES parameters.
• Utilized linear integer programming for solving the event alignment problem.

Main Results:

• N-variate SES yields more reliable similarity estimates than bivariate SES on synthetic data.
• Applied N-variate SES to quantify firing reliability in Morris-Lecar neurons.
• Detected anomalies in EEG synchrony for patients with mild cognitive impairment using N-variate SES.

Conclusions:

• The proposed N-variate SES method effectively extends similarity analysis to multiple time series.
• N-variate SES offers improved reliability and more detailed insights compared to bivariate SES.
• This approach has significant potential for complex systems analysis in neuroscience and beyond.