Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models

Sirio Legramanti (), Tommaso Rigon and Daniele Durante ()
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Sirio Legramanti: Bocconi University
Tommaso Rigon: Duke University
Daniele Durante: Bocconi University

Sankhya A: The Indian Journal of Statistics, 2022, vol. 84, issue 1, No 4, 108-126

Abstract: Abstract Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of knowledge are typically included in the model to supervise the cluster assignment mechanism or to improve inference on edge probabilities. Although these solutions are routinely implemented, there is a lack of formal approaches to test if a given external node partition is in line with the endogenous clustering structure encoding stochastic equivalence patterns among the nodes in the network. To fill this gap, we develop a formal Bayesian testing procedure which relies on the calculation of the Bayes factor between a stochastic block model with known grouping structure defined by the exogenous node partition and an infinite relational model that allows the endogenous clustering configurations to be unknown, random and fully revealed by the block–connectivity patterns in the network. A simple Markov chain Monte Carlo method for computing the Bayes factor and quantifying uncertainty in the endogenous groups is proposed. This strategy is evaluated in simulations, and in applications studying brain networks of Alzheimer’s patients.

Keywords: Bayes factor; Brain network; Chinese restaurant process; Infinite relational model; Stochastic equivalence; Primary 62-XX; Secondary 62F15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13171-020-00231-2

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