Percolation Thresholds of Updated Posteriors for Tracking Causal Markov Processes in Complex Networks

TL;DR

This paper introduces conditions for phase transitions in the updated posterior of node states in complex networks, improving the modeling of dynamic processes like epidemics through active monitoring and intervention strategies.

Contribution

It presents novel conditions for observation-dependent percolation thresholds in updated posteriors, enhancing understanding of network dynamics under active monitoring.

Findings

Derived conditions for observation-dependent phase transitions

Improved modeling of network responses to interventions

Insights into dynamic tracking of causal processes

Abstract

Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since traditional percolation thresholds are derived using observation independent Markov chains, the threshold of the posterior should more accurately model the true phase transition of a network, as the updated posterior more accurately tracks the process. These conditions should provide insight into modeling the dynamic response of the updated posterior to active intervention and control policies while monitoring large complex networks.