AI 中文总结
研究从匿名汇总信念数据识别贝叶斯主体群体信念分布的问题，利用图论结构判断识别情况，确立了从汇总信念数据恢复信念异质性的限制与设计原则。
AI 中文摘要
我们研究从匿名汇总信念数据中识别贝叶斯主体群体中的信念分布。虽然单个贝叶斯主体的完整信念可从对适当二元事件集合的信念中恢复，但此原则不一定适用于群体：信念的逐个事件分布可能无法识别先验的潜在分布。我们研究这种失败何时是普遍的，何时是例外的。识别由状态空间上观察到的事件族诱导的图论结构决定。在n主体分布中，如果诱导图是非可分的，识别是普遍的；如果图是可分的，非识别是普遍的。结果确立了从汇总信念数据中恢复信念异质性的限制和设计原则。
英文摘要
We study the identification of belief distributions in a population of Bayesian agents from anonymous aggregate belief data. While a single Bayesian agent's full belief can be recovered from beliefs over a suitable collection of binary events, this principle need not extend to populations: event-by-event distributions of beliefs may fail to identify the underlying distribution of priors. We study when this failure is generic and when it is exceptional. Identification is governed by the graph-theoretic structure induced by the observed family of events on the state space. Among $n$-agent distributions, identification is generic if the induced graph is nonseparable, while non-identification is generic if the graph is separable. The results establish both limits and design principles for recovering belief heterogeneity from aggregate belief data.
