Volume 24, 2020
|Page(s)||138 - 147|
|Published online||03 March 2020|
A note on perfect simulation for Exponential Random Graph Models
Statistics Department, Universidade Federal de São Carlos,
São Carlos, Brazil.
2 Unité de Mathématiques Pures et Appliquées, Laboratoire de l’Informatique du Parallélisme, Ecole Normale Supérieure de Lyon, Université de Lyon, Lyon, France.
3 Statistics Department, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil.
* Corresponding author: firstname.lastname@example.org
Accepted: 6 November 2019
In this paper, we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling from the past method of Propp and Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.
Mathematics Subject Classification: 60K35 / 60J22
Key words: Exponential Random Graph / perfect simulation / coupling from the past / MCMC / Glauber dynamics
© EDP Sciences, SMAI 2020
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