Bayesian Model Selection for Exponential Random Graph Models via Adjusted Pseudolikelihoods
Bayesian Model Selection for Exponential Random Graph Models via Adjusted Pseudolikelihoods
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DOI：
10.1080/10618600.2018.1448832
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发表时间：
2018-01-01
影响因子：
2.4
通讯作者：
Maire, Florian
中科院分区：
文献类型：
--
作者：
Bouranis, Lampros;Friel, Nial;Maire, Florian
具有棘手似然函数的模型出现在网络分析和空间统计等领域，特别是涉及吉布斯随机场的领域。后验参数估计在这些设置被称为一个双重棘手的问题，因为这两个似然函数和后验分布是棘手的。贝叶斯模型的比较通常基于统计证据，即模型参数上的未归一化后验分布的积分，这种积分很少以封闭形式提供。对于双重棘手的模型，估计证据增加了另一层难度。因此，在用于网络分析的指数随机图模型的集合中选择最好地描述所观察到的网络的模型是一项艰巨的任务。伪似然提供了一个易于处理的近似的可能性，但应谨慎对待，因为他们可能会导致不合理的推断。本文指定了一种方法来调整pseudolikelihoods，以获得合理的，但易于处理的，近似的可能性。这允许实现广泛使用的计算方法的证据估计和追求贝叶斯模型选择指数随机图模型的分析社交网络。与现有方法的实证比较表明，我们的程序产生类似的证据估计，但在较低的计算成本。这篇文章的补充材料可在网上查阅。
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter estimation in these settings is termed a doubly intractable problem because both the likelihood function and the posterior distribution are intractable. The comparison of Bayesian models is often based on the statistical evidence, the integral of the un-normalized posterior distribution over the model parameters which is rarely available in closed form. For doubly intractable models, estimating the evidence adds another layer of difficulty. Consequently, the selection of the model that best describes an observed network among a collection of exponential random graph models for network analysis is a daunting task. Pseudolikelihoods offer a tractable approximation to the likelihood but should be treated with caution because they can lead to an unreasonable inference. This article specifies a method to adjust pseudolikelihoods to obtain a reasonable, yet tractable, approximation to the likelihood. This allows implementation of widely used computational methods for evidence estimation and pursuit of Bayesian model selection of exponential random graph models for the analysis of social networks. Empirical comparisons to existing methods show that our procedure yields similar evidence estimates, but at a lower computational cost. Supplementary material for this article is available online.