  This paper deals with the modeling and estimation of the sociological
phenomena called echo chambers and segregation in social networks.
Specifically, we present a novel community-based graph model that represents
the emergence of segregated echo chambers as a Markov bridge process. A Markov
bridge is a one-dimensional Markov random field that facilitates modeling the
formation and disassociation of communities at deterministic times which is
important in social networks with known timed events. We justify the proposed
model with six real world examples and examine its performance on a recent
Twitter dataset. We provide model parameter estimation algorithm based on
maximum likelihood and, a Bayesian filtering algorithm for recursively
estimating the level of segregation using noisy samples obtained from the
network. Numerical results indicate that the proposed filtering algorithm
outperforms the conventional hidden Markov modeling in terms of the
mean-squared error. The proposed filtering method is useful in computational
social science where data-driven estimation of the level of segregation from
noisy data is required.
