Detecting zealots in the Noisy Voter Model using Bayesian inference

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
dfferent 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 Erdos-Renyi
networks, showing how the performance of the method depends on the network connectivity.