Detecting zealots in the Noisy Voter Model using Bayesian inference

Abstract

[eng] The aim of this work is to show Bayesian inference as an useful tool to detect zealots in the noisy voter model. We present a method based on the simulation of this stochastic process and the periodic measurement of n, the number of agents in state 1. We calibrate the method so we require the least number of observations to detect zealots to a given precision. After the method’s calibration, we investigate its performance in fully connected networks for different combinations of zealots. We show that the performance of the method is significantly different when detecting one single type of zealots than when detecting both types. The existence of a transition in the system for which the stationary probability distributions for n undergo a change of shape (criticality) plays a role in the detection when there are zealots of one single type (or no zealots at all) in the system, but it has not any effect when there are zealots of both types. Finally, we briefly explore how the method works in Erd¨os-R´enyi networks, showing how the performance of the method depends on the network connectivity