Estimating inter-event time distributions from finite observation periods in communication networks

TL;DR

This paper addresses the bias in estimating inter-event time distributions from finite observation windows in communication networks, proposing correction methods that improve accuracy in understanding human communication patterns.

Contribution

It introduces a bias correction approach for IET distributions in finite data, applicable without assuming specific distribution shapes, and demonstrates its effectiveness on empirical communication data.

Findings

Finite observation windows bias IET variance estimates.

Correcting bias alters the perceived tail behavior of IET distributions.

Bias correction can significantly impact models of human communication and information spreading.

Abstract

A diverse variety of processes --- including recurrent disease episodes, neuron firing, and communication patterns among humans --- can be described using inter-event time (IET) distributions. Many such processes are ongoing, although event sequences are only available during a finite observation window. Because the observation time window is more likely to begin or end during long IETs than during short ones, the analysis of such data is susceptible to a bias induced by the finite observation period. In this paper, we illustrate how this length bias is born and how it can be corrected without assuming any particular shape for the IET distribution. To do this, we model event sequences using stationary renewal processes, and we formulate simple heuristics for determining the severity of the bias. To illustrate our results, we focus on the example of empirical communication networks, which are temporal networks that are constructed from communication events. The IET distributions of such systems guide efforts to build models of human behavior, and the variance of IETs is very important for estimating the spreading rate of information in networks of temporal interactions. We analyze several well-known data sets from the literature, and we find that the resulting bias can lead to systematic underestimates of the variance in the IET distributions and that correcting for the bias can lead to qualitatively different results for the tails of the IET distributions.