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

Type
Article

Authors
Jin, Ick Hoon
Liang, Faming
Yuan, Ying

KAUST Grant Number
KUS-C1-016-04

Date
2013

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.

Citation
Jin IH, Liang F, Yuan Y (2013) Bayesian analysis for exponential random graph models using the adaptive exchange sampler. Statistics and Its Interface 6: 559–576. Available: http://dx.doi.org/10.4310/sii.2013.v6.n4.a13.

Acknowledgements
Yuan and Jin acknowledge support from the NIH grant R01CA154591.Liang’s research was partially supported by grants from the NationalScience Foundation (DMS-1007457, DMS-1106494 and DMS-1317131)and the award (KUS-C1-016-04) made by King Abdullah Universityof Science and Technology (KAUST)

Publisher
International Press of Boston

Journal
Statistics and Its Interface

DOI
10.4310/sii.2013.v6.n4.a13

PubMed ID
24653788

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