Partial orders are a natural model for the social hierarchies that may constrain "queue-like" rank-order data. However, the computational cost of counting the linear extensions of a general partial order on a ground set with more than a few tens of elements is prohibitive. Vertex-series-parallel partial orders (VSPs) are a subclass of partial orders which admit rapid counting and represent the sorts of relations we expect to see in a social hierarchy. However, no Bayesian analysis of VSPs has been given to date. We construct a marginally consistent family of priors over VSPs with a parameter controlling the prior distribution over VSP depth. The prior for VSPs is given in closed form. We extend an existing observation model for queue-like rank-order data to represent noise in our data and carry out Bayesian inference on "Royal Acta" data and Formula 1 race data. Model comparison shows our model is a better fit to the data than Plackett-Luce mixtures, Mallows mixtures, and "bucket order" models and competitive with more complex models fitting general partial orders.

翻译：偏序集是约束"队列型"排序数据的社会层级结构的自然模型。然而，对于包含数十个以上元素的基础集合，计算一般偏序集线性扩展的计数成本极其高昂。顶点-串行-并行偏序集（VSPs）作为偏序集的一个子类，不仅支持快速计数，更能表征社会层级中预期出现的各类关系。目前尚缺乏针对VSPs的贝叶斯分析方法。我们构建了一个边际一致的VSP先验族，其中包含控制VSP深度先验分布的参数，该先验以闭合形式给出。我们将现有的队列型排序数据观测模型扩展至包含数据噪声表征，并基于"皇家法令"数据集与一级方程式赛车数据开展贝叶斯推断。模型比较表明，相较于Plackett-Luce混合模型、Mallows混合模型及"桶序"模型，本模型对数据的拟合效果更优，且与拟合一般偏序集的复杂模型性能相当。