Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new dynamic network model classes exploiting the Generalized Poisson distribution to capture both under- and overdispersion. We consider three different dynamic specifications: latent factor dynamics, autoregressive dynamics, and latent position dynamics, and study some theoretical properties of the random networks, showing the impact of the dispersion parameter on the random network's connectivity. After discussing the parameter identification strategy, we present a Bayesian inference procedure along with a posterior sampling algorithm. A numerical illustration demonstrates the effectiveness of the designed algorithm and provides estimates of the misspecification bias when unequal dispersion is neglected. Our new models are then applied to two relevant dynamic datasets considered in previous studies: a set of bike-sharing dynamic networks and a set of dynamic media networks. Our results highlight the importance of explicitly modeling overdispersion for both an accurate in-sample fit and out-of-sample performance.

翻译：计数加权时间网络中的边权重通常呈现不等的离散程度，这种不均等性无法仅通过以条件均值中的潜在因子对观测异质性进行建模来完全解释。为此，我们提出利用广义泊松分布来刻画欠离散与过离散现象的新型动态网络模型类别。我们考虑了三种不同的动态设定：潜在因子动态、自回归动态和潜在位置动态，并研究了随机网络的若干理论性质，揭示了离散参数对随机网络连通性的影响。在讨论参数识别策略后，我们给出了贝叶斯推断流程及后验采样算法。数值模拟表明所设计算法的有效性，并提供了忽略不等离散度时设定偏差的估计值。随后将新模型应用于两项已有研究中的相关动态数据集：一组共享单车动态网络与一组动态媒体网络。研究结果凸显了显式建模过离散现象对实现精确的样本内拟合与样本外性能的重要性。