Simulation-consistent Estimation of the Marginal Likelihood for Block Models

2026-07-27

AI Summary

This study addresses the challenges of marginal likelihood estimation for block models under fixed data size, particularly those arising from label switching and high-dimensional components. The authors propose a novel method based on MCMC samples that constructs a label-switching-invariant estimator, ensuring consistency, asymptotic normality, and finite variance under finite-sample settings while maintaining strong scalability. In simulations, the approach accurately recovers known analytical solutions, and when applied to real-world COP28 social network data, it effectively uncovers latent community structures. This provides a reliable tool for model selection in complex network analysis.

Abstract

We propose a methodology for computing marginal likelihoods for block models. The proposed estimator computes the marginal likelihood from Markov chain Monte Carlo (MCMC) samples and is simulation-consistent, even when the size of the dataset is fixed. Moreover, it is asymptotically normal, of finite variance, invariant to label switching and can be computed efficiently, even for models with an arbitrarily large number of components. We evaluate the method through simulation studies in settings where the true marginal likelihood is available analytically. Finally, we apply the approach to a social network dataset based on the 2023 United Nations Climate Change Conference (COP28) and discuss the resulting insights.

Problem

• marginal likelihood
• block models
• simulation-consistent estimation
• MCMC
• label switching

Innovation

• simulation-consistent
• marginal likelihood
• block models
• MCMC
• label switching invariance