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：计数加权时间网络通常表现出边权的不等离散性，这种离散性无法通过条件均值中的潜在因子对观测异质性进行建模而完全解释。因此，我们提出利用广义泊松分布捕获欠离散和过离散的新型动态网络模型类。我们考虑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，并研究随机网络的若干理论性质，揭示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，我们提出一个贝叶斯推断过程及其后验采样算法。数值示例展示了所设计算法的有效性，并提供了忽略不等离散性时的误设偏差估计。随后，我们将新模型应用于两项先前的相关动态数据集：一组共享单车动态网络和一组动态媒体网络。我们的结果强调了对过离散进行显式建模的重要性，这能同时提升样本内拟合精度和样本外预测性能。