Efficient Bayesian inference for multiple network data

2026-10-01

AI Summary

This study addresses the computational bottlenecks in efficient Bayesian inference for multi-network data. To overcome this challenge, we propose a semi-conjugate Bayesian modeling framework based on the central Erdős–Rényi distribution, which integrates Gibbs sampling with empirical Bayes estimation to enable efficient posterior inference. The methodology is implemented in the R package BayesCER. By leveraging the proposed semi-conjugate prior design, the approach significantly reduces computational complexity while accurately recovering network summary statistics. Furthermore, the empirical Bayes method maintains robust performance as network size scales, demonstrating strong scalability. This work provides a practical tool that effectively balances statistical accuracy and computational efficiency for large-scale network analysis.

Abstract

We investigate distributional properties of the centered Erdős--Rényi distribution (Lunagòmez et al., 2021) and propose a semi-conjugate Bayesian approach to multiple network data. In simulations, both Gibbs sampling and empirical Bayes accurately recover network summaries, with the latter scaling efficiently with network size. As a companion to this note, we provide the R package BayesCER, which implements the proposed methodology.

Problem

• Bayesian inference
• multiple network data
• centered Erdős–Rényi distribution

Innovation

• Bayesian inference
• multiple network data
• centered Erdős–Rényi distribution
• semi-conjugate
• empirical Bayes