标题： 大样本下基于合并模型推断的成本泛函分析 显示英文标题

标题： Large-sample analysis of cost functionals for inference under the coalescent

摘要： 合并模型是中性进化下潜在基因树的基础模型，但其抽样概率难以处理。近似这些抽样概率的方法要么引入偏差，要么无法扩展到大样本量。我们证明了带有复发突变和有限数量等位基因的合并模型的一类成本泛函在无限样本极限下收敛到易于处理的过程。特定的成本选择提供了关于重要性采样方法的见解，这是合并模型抽样概率近似的经典工具。这些见解揭示了合并模型重要性采样算法的行为与标准顺序重要性采样器（带或不带重采样）明显不同。我们进行了一项模拟研究来验证我们的渐近性对于有限（且适度）样本量的算法是准确的。我们的结果还促进了合并序列重要性采样的计算资源先验优化。我们在无限位点模型下的重要性采样方法中没有观察到相同的行为，该模型在大多数方面被视为有限等位基因突变的良好且更易处理的近似值。 显示英文摘要

摘要： The coalescent is a foundational model of latent genealogical trees under neutral evolution, but suffers from intractable sampling probabilities. Methods for approximating these sampling probabilities either introduce bias or fail to scale to large sample sizes. We show that a class of cost functionals of the coalescent with recurrent mutation and a finite number of alleles converge to tractable processes in the infinite-sample limit. A particular choice of costs yields insight about importance sampling methods, which are a classical tool for coalescent sampling probability approximation. These insights reveal that the behaviour of coalescent importance sampling algorithms differs markedly from standard sequential importance samplers, with or without resampling. We conduct a simulation study to verify that our asymptotics are accurate for algorithms with finite (and moderate) sample sizes. Our results also facilitate the a priori optimisation of computational resource allocation for coalescent sequential importance sampling. We do not observe the same behaviour for importance sampling methods under the infinite sites model of mutation, which is regarded as a good and more tractable approximation of finite alleles mutation in most respects.