Longitudinal network models and permutation‐uniform Markov chains
研究了纵向网络中边随时间开关的马尔可夫链，发现其联合分布也是指数族，并引入置换均匀子类简化分析，适用于时间指数随机图模型，可推导闭式极大似然估计。
Abstract Consider longitudinal networks whose edges turn on and off according to a discrete‐time Markov chain with exponential‐family transition probabilities. We characterize when their joint distributions are also exponential families with the same parameter, improving data reduction. Further we show that the permutation‐uniform subclass of these chains permit interpretation as an independent, identically distributed sequence on the same state space. We then apply these ideas to temporal exponential random graph models, for which permutation uniformity is well suited, and discuss mean‐parameter convergence, dyadic independence, and exchangeability. Our framework facilitates our introducing a new network model; simplifies analysis of some network and autoregressive models from the literature, including by permitting closed‐form expressions for maximum likelihood estimates for some models; and facilitates applying standard tools to longitudinal‐network Markov chains from either asymptotics or single‐observation exponential random graph models.