Quantifying statistical interdependence by message passing on graphs-part I: one-dimensional point processes.

Area of Science:

• Time Series Analysis
• Statistical Physics
• Computational Neuroscience

Background:

• Quantifying statistical interdependence between time series is crucial in various scientific fields.
• Classical measures may not robustly capture the nuances of event synchrony and reliability.

Purpose of the Study:

• To introduce a novel method, stochastic event synchrony (SES), for quantifying the statistical interdependence of two time series.
• To develop a robust approach for analyzing event alignment, timing precision, and reliability in time series data.

Main Methods:

• Extracting two time series for analysis.
• Aligning events between series using the max product algorithm.
• Quantifying similarity via parameters like time delay, time jitter variance, and event coincidence fraction.
• Computing SES parameters using maximum a posteriori (MAP) estimation.

Main Results:

• Demonstrated SES's ability to quantify timing precision and event reliability robustly using surrogate data.
• Validated the method's effectiveness on simulated neuronal spike data from the Morris-Lecar neuron model.
• Showcased SES as a more sensitive measure compared to classical approaches.

Conclusions:

• Stochastic event synchrony (SES) provides a powerful and robust framework for analyzing the interdependence of time series.
• The method offers significant advantages in quantifying event alignment and reliability, particularly in neuroscience applications.
• SES represents a significant advancement in time series analysis for event-based data.