Understanding the heavy-tailed dynamics in human behavior

The recent availability of electronic data sets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of data sets, the interevent times between consecutive communication events obey heavy-tailed power law dynamics. Explaining this has proved controversial, and two distinct hypotheses have emerged. The first holds that these power laws are fundamental, and arise from the mechanisms such as priority queuing that humans use to schedule tasks. The second holds that they are statistical artifacts which only occur in aggregated data when features such as circadian rhythms and burstiness are ignored. We use a large social media data set to test these hypotheses, and find that although models that incorporate circadian rhythms and burstiness do explain part of the observed heavy tails, there is residual unexplained heavy-tail behavior which suggests a more fundamental cause. Based on this, we develop a quantitative model of human behavior which improves on existing approaches and gives insight into the mechanisms underlying human interactions.

Figure 1

Example data for four Twitter users. Each plot represents the event sequence of one user, where each row is a single day and the days are stacked on top of each other. Dots represent the times at which each user made tweets.

Figure 2

Empirical density (black line) of the logarithm of the interevent times for each of the four users, on a logarithmic scale. The dotted red line denotes the best-fitting log-exponential distribution (note: the logarithmic transformation has been used to aid interpretation, and all logarithms are in base $e$).

Figure 3

Empirical density (black line) of the logarithm of the active-state interevent times for each of the four users, after fitting the simple Poissonian burst model. The dotted red line denotes the best-fitting log-exponential distribution (note: the logarithmic transformation has been used to aid interpretation).

Figure 4

Empirical density (black line) of the logarithm of the active-state interevent times for each of the four users, after fitting the HMM using the lognormal distribution. The dotted red line denotes the best-fitting lognormal distribution (note: the logarithmic transformation has been used to aid interpretation).

Figure 5

Event times for the four Twitter users, with the events produced during active states according to the best-fitting lognormal HMM model colored in red (dark gray in gray scale).