双总体基准测试模型
The Dual-Population Benchmark Model
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中文总结 AI 辅助
本文提出双总体基准测试的平面泊松过程模型，利用选择算子划分正分量未来点的排序类别，丰富贝叶斯分布自由推断工具库，明确顺序与可交换性的关系。
中文摘要 AI 辅助
受费希尔（Fisher）和希尔（Hill）关于排序及枢轴量思想的启发，我们引入了一个平面泊松过程（PPP）模型：其中负分量Π₋在选择算子C的作用下，提供一组过去的基准，这些基准将正分量Π₊的未来点划分为不同的排序类别。这些基准在有序 paintbox 中充当分隔符，同时兼具选择算子确立的过去标准的双重作用。平面泊松过程的特殊同质性特性提供了无穷多的可能性，涵盖了许多现有组合结构，并丰富了贝叶斯分布自由推断的工具库。本文考虑的一种特定基准生成机制（指数竞赛）等价于按非均匀顺序统计量的间距进行划分的装置。在方法论层面，本文旨在强调顺序作为可交换结构的重要特征，其与基于分量大小的描述互为补充。此外，我们主张：由潜在强度参数诱导的顺序本质上继承自遥远过去的时间采样顺序，因此解耦的顺序可在总体对偶框架中共存，而不会干扰分量的大小偏差性及样本内的完全可交换性。这意味着非线性 CRP 中分量的不可区分性（有时被视为不可交换性）实际上并未破坏可交换性，应在有序结构范式内与到达顺序相协调。
英文摘要
Motivated by Fisher's and Hill's \cite{Fisher,Hill} ideas of ranking and pivotal quantities, we introduce a planar Poisson process (PPP) model in which the negative component \(Π_-\), acted upon by a choice operator {\rm C}, supplies a set of past benchmarks that divide the future points of the positive component \(Π_+\) into ranked categories. The benchmarks act as separators in an ordered paintbox while simultaneously acquiring the dual role of past standards established by the choice operator. The exceptional homogeneity properties of the PPP offer an infinitude of possibilities which absorb many existing combinatorial structures and enrich the toolbox of Bayesian distribution-free inference. A particular benchmark generating mechanism considered here (the exponential race) amounts to the device of splitting into spacings of nonhomogeneous order statistics. On the methodological side, the paper aims to highlight the role of order as important characteristic of an exchangeable structure, complementary to the description in terms of the components size. Moreover, we advocate the viewpoint that the order induced by a latent strength parameter is {\it intrinsically} inherited from the distant-past temporal sampling order, hence the decoupled orders may coexist within the framework of population duality without disturbing size-biasedness of components and the full exchangeability within the sample. This implies that the indistinguishability of components in the nonlinear CRP, sometimes regarded as nonexchangeability, does not in fact destroy exchangeability and should be reconciled with the arrival ordering within the paradigm of ordered structures.
