论文标题
多元PUPUR-PIRTH物种模型的参数可识别性
Parameter Identifiability of a Multitype Pure-Birth Model of Speciation
论文作者
论文摘要
多元化模型描述了进化树的随机生长，通过形成和灭绝事件对物种的历史关系进行建模。一类此类模型允许树木内物种的独立特征或类型的形成率和灭绝率所取决于。尽管参数的可识别性对于使用模型证明参数估计的合理性是必要的，但尽管采用了推断，但尚未为这些模型正式建立。这项工作建立了通用的可识别性，以标记交换这种模型的简单形式之一的参数，即从单个树观测中得出的渐近分布，即其深度为Infinity。至关重要的是，对于可用数据的应用，在树上的任何内部也不需要观察类型，甚至不需要在叶子上观察。
Diversification models describe the random growth of evolutionary trees, modeling the historical relationships of species through speciation and extinction events. One class of such models allows for independently changing traits, or types, of the species within the tree, upon which speciation and extinction rates depend. Although identifiability of parameters is necessary to justify parameter estimation with a model, it has not been formally established for these models, despite their adoption for inference. This work establishes generic identifiability up to label swapping for the parameters of one of the simpler forms of such a model, a multitype pure birth model of speciation, from an asymptotic distribution derived from a single tree observation as its depth goes to infinity. Crucially for applications to available data, no observation of types is needed at any internal points in the tree, nor even at the leaves.
