Statistics and Its Interface

Volume 6 (2013)

Number 4

Bayesian analysis for exponential random graph models using the adaptive exchange sampler

Pages: 559 – 576

DOI: http://dx.doi.org/10.4310/SII.2013.v6.n4.a13

Authors

Ick Hoon Jin (Department of Biostatistics, The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A.)

Faming Liang (Department of Statistics, Texas A&M University, College Station, Texas, U.S.A.)

Ying Yuan (Department of Biostatistics, The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A.)

Abstract

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the issue of intractable normalizing constants encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

Keywords

exchange algorithm, exponential random graph model, adaptive Markov chain Monte Carlo, social network

2010 Mathematics Subject Classification

Primary 65C05. Secondary 05C80.

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