Asymptotic uncertainty quantification for communities in sparse planted bi-section models

Posterior distributions for community structure in sparse planted bi-section models are shown to achieve exact (resp. almost-exact) recovery, with sharp bounds the sparsity regimes where edge probabilities decrease as O(log(n)/n) O(1/n)). Assuming posterior one may interpret credible sets enlarged sets) asymptotically consistent confidence sets; diameters of those controlled by rate concentration. If levels chosen grow quickly enough, corresponding can be interpreted frequentist without conditions on In O(1/n) sparsity, or when within-community and between-community very close, asymptotic coverage, also