We give a new class of models for time series data in which actors are listed in order of precedence. We model the lists as a realisation of a queue in which queue-position is constrained by an underlying social hierarchy. We model the hierarchy as a partial order so that the lists are random linear extensions. We account for noise via a random queue-jumping process. We give a marginally consistent prior for the stochastic process of partial orders based on a latent variable representation for the partial order. This allows us to introduce a parameter controlling partial order depth and incorporate actor-covariates informing the position of actors in the hierarchy. We fit the model to witness lists from Royal Acta from England, Wales and Normandy in the eleventh and twelfth centuries. Witnesses are listed in order of social rank, with any bishops present listed as a group. Do changes in the order in which the bishops appear reflect changes in their personal authority? The underlying social order which constrains the positions of bishops within lists need not be a complete order and so we model the evolving social order as an evolving partial order. The status of an Anglo-Norman bishop was at the time partly determined by the length of time they had been in office. This enters our model as a time-dependent covariate. We fit the model, estimate partial orders and find evidence for changes in status over time. We interpret our results in terms of court politics. Simpler models, based on Bucket Orders and vertex-series-parallel orders, are rejected. We compare our results with a time-series extension of the Plackett-Luce model.

翻译：我们提出了一类面向时间序列数据的新模型，其中行为者按照优先顺序排列。我们将这些列表建模为队列的实现，该队列中的位置受潜在社会等级约束。我们将社会等级建模为部分有序关系，从而使列表成为随机线性拓展。我们通过随机插队过程考虑噪声因素。基于部分有序关系的潜变量表示，我们给出了部分有序随机过程的边际一致先验。由此可以引入控制部分有序深度的参数，并融入指示行为者在等级中位置的行为者协变量。我们将该模型应用于11至12世纪英格兰、威尔士和诺曼底《皇家法令》中的见证人名单。见证人按社会地位排序，列席主教以群体形式出现。主教出现顺序的变化是否反映了其个人权威的变迁？约束主教在列表中位置的潜在社会秩序不必是完全有序的，因此我们将演化的社会秩序建模为演化的部分有序关系。盎格鲁-诺曼主教当时的地位部分取决于其任职时长。这一信息以时变协变量的形式纳入模型。通过拟合模型、估计部分有序关系，我们发现了地位随时间变化的证据。我们结合宫廷政治对结果进行解读。基于桶序和顶点-级联序的简化模型被否决。我们还将结果与Plackett-Luce模型的时间序列扩展进行了比较。