## Bayesian Analysis

### Bayesian Community Detection

#### Abstract

We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities. We show that this estimator is strongly consistent when the expected degree is at least of order $\log^{2}{n}$, where $n$ is the number of nodes in the network.

#### Article information

Source
Bayesian Anal., Volume 13, Number 3 (2018), 767-796.

Dates
First available in Project Euclid: 19 October 2017

https://projecteuclid.org/euclid.ba/1508378465

Digital Object Identifier
doi:10.1214/17-BA1078

Mathematical Reviews number (MathSciNet)
MR3807866

Subjects
Primary: 62F15: Bayesian inference 90B15: Network models, stochastic

#### Citation

van der Pas, S. L.; van der Vaart, A. W. Bayesian Community Detection. Bayesian Anal. 13 (2018), no. 3, 767--796. doi:10.1214/17-BA1078. https://projecteuclid.org/euclid.ba/1508378465

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