Bayesian inference for partial orders from random linear extensions: power relations from 12th Century Royal Acta
由随机线性扩展推断偏序：十二世纪王室文书中的权力关系AI 解读 ↓
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由随机线性扩展推断偏序：十二世纪王室文书中的权力关系
- 研究问题
- 历史文书中的见证人排序可能只反映部分社会等级约束；如何据此推断随时间演变的权威结构，并量化地位变化？
- 方法与思路
- 作者构建隐藏状态为动态偏序集的隐马尔可夫模型，观测为遵循偏序的名单，并用随机插队过程描述排序噪声。
- 材料陈述的贡献
- 摘要称模型推广现有排序数据模型，纳入人物协变量并发现地位变化证据，比较了简化偏序模型及动态 Plackett–Luce 模型。
- 阅读关注点
- 应核对名单生成机制、日期区间的处理、偏序先验与层级深度参数，以及模型比较证据如何支持历史地位变化的解释。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审与期刊接收状态未核实；摘要未说明模型识别、后验计算细节或拒绝简化模型的标准。
原文摘要
In the eleventh and twelfth centuries in England, Wales and Normandy, Royal Acta were legal documents in which witnesses were listed in order of social status. Any bishops present were listed as a group. For our purposes, each witness-list is an ordered permutation of bishop names with a known date or date-range. Changes over time in the order bishops are listed may reflect changes in their authority. Historians would like to detect and quantify these changes. There is no reason to assume that the underlying social order which constrains bishop-order within lists is a complete order. We therefore model the evolving social order as an evolving partial ordered set or {\it poset}. We construct a Hidden Markov Model for these data. The hidden state is an evolving poset (the evolving social hierarchy) and the emitted data are random total orders (dated lists) respecting the poset present at the time the order was observed. This generalises existing models for rank-order data such as Mallows and Plackett-Luce. We account for noise via a random ``queue-jumping'' process. Our latent-variable prior for the random process of posets is marginally consistent. A parameter controls poset depth and actor-covariates inform the position of actors in the hierarchy. We fit the model, estimate posets 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. Our software is publicly available.