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 intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues 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.

中文翻译：

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使用自适应交换采样器对指数随机图模型进行贝叶斯分析

指数随机图模型已广泛应用于社交网络分析。然而，由于难以处理的归一化常数和模型简并性，从统计的角度来看，这些模型极难处理。在本文中，我们考虑使用自适应交换采样器对指数随机图模型进行完全贝叶斯分析，该分析解决了马尔可夫链蒙特卡罗 (MCMC) 模拟中遇到的棘手的归一化常数和模型退化问题。自适应交换采样器可以看作是交换算法的 MCMC 扩展，它通过并行运行的辅助马尔可夫链的重要性采样过程生成辅助网络。该算法的收敛性是在温和条件下建立的。自适应交换采样器使用一些社交网络进行说明，包括佛罗伦萨商业网络、分子合成网络和海豚网络。结果表明自适应交换算法可以比近似交换算法产生更准确的估计，同时保持相同的计算效率。