标题： 可交换下概率 显示英文标题

标题： Exchangeable lower previsions

摘要： 我们将 de Finetti（1937）关于可交换性的概念扩展到有限和可数变量序列，当主体对它们的信念使用一致的下概率模型而不是（线性）概率时。 我们在有限和可数情况下分别证明了表示定理，分别涉及无放回和有放回抽样。 我们还建立了可交换序列样本均值的收敛结果。 最后，我们研究并解决了可交换自然扩展问题：如何找到最保守（逐点最小）的一致且可交换的下概率，该下概率支配给定的下概率。 显示英文摘要

摘要： We extend de Finetti's (1937) notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We prove representation theorems in both the finite and the countable case, in terms of sampling without and with replacement, respectively. We also establish a convergence result for sample means of exchangeable sequences. Finally, we study and solve the problem of exchangeable natural extension: how to find the most conservative (point-wise smallest) coherent and exchangeable lower prevision that dominates a given lower prevision.