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Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

Ick Hoon Jin1, Ying Yuan1, Faming Liang2

  • 1Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030-4009, USA.

Statistics and Its Interface
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Summary
This summary is machine-generated.

This study introduces an adaptive exchange sampler for exponential random graph models, overcoming statistical challenges in network analysis. The new method provides more accurate estimates for social network data with efficient computation.

Keywords:
Adaptive Markov chain Monte CarloExchange AlgorithmExponential Random Graph ModelSocial Network

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Area of Science:

  • Network analysis
  • Statistical modeling
  • Computational statistics

Background:

  • Exponential random graph models (ERGMs) are prevalent in social network analysis.
  • ERGMs present statistical challenges due to intractable normalizing constants and model degeneracy.
  • Existing Markov chain Monte Carlo (MCMC) methods struggle with these ERGM complexities.

Purpose of the Study:

  • To develop a fully Bayesian approach for ERGMs.
  • To address the normalizing constant and degeneracy issues in ERGM simulations.
  • To introduce a novel MCMC method for improved statistical analysis of networks.

Main Methods:

  • Utilized an adaptive exchange sampler, an extension of the exchange algorithm.
  • Employed importance sampling from parallel auxiliary Markov chains to generate auxiliary networks.
  • Established theoretical convergence guarantees under mild conditions.

Main Results:

  • The adaptive exchange sampler effectively resolves normalizing constant and degeneracy problems in ERGMs.
  • Demonstrated improved accuracy of estimates compared to approximate exchange algorithms.
  • Maintained computational efficiency comparable to existing methods.

Conclusions:

  • The adaptive exchange sampler offers a robust and accurate Bayesian inference method for ERGMs.
  • This approach enhances the statistical analysis of complex network data.
  • The method is validated on real-world networks like the Florentine business network.