Stochastic modeling of a serial killer

TL;DR

This paper models a serial killer's activity as a neural threshold process, explaining the power-law distribution of inter-murder intervals and the 'Devil's staircase' pattern observed in their crime timeline.

Contribution

It introduces a neural excitation-based stochastic model that accounts for the timing patterns of serial murders, supported by empirical data and simulations.

Findings

Inter-murder intervals follow a power law with exponent 1.4.

Cumulative murders exhibit a 'Devil's staircase' pattern.

Model simulations align with observed data from multiple serial killers.

Abstract

We analyze the time pattern of the activity of a serial killer, who during twelve years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of "Devil's staircase" type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis.