同源数据的随机Dollo模型中的缺失数据及其在原始印欧语系定年中的应用
Missing data in a stochastic Dollo model for cognate data, and its application to the dating of Proto-Indo-European
摘要：
Nicholls和Gray（2008）描述了性状数据的系统发育模型。他们使用他们的模型从词汇数据中估计印欧语言树的分支时间。Alekseyenko等人（2008年）扩展了该模型并将其应用于遗传学。在本文中，我们扩展的推理处理数据随机缺失。当trait数据被收集时，trait会以一种依赖于trait和缺失数据内容的方式进行细化。Nicholls and Gray（2008）将缺失的记录视为缺失的性状。赫梯人有12%的缺失特征记录。它的年龄在交叉验证中预测得很差。我们的预测与历史记录是一致的。Nicholls and Gray（2008）删除了7种语言，因为它们有太多的缺失数据。我们将所有24种语言都拟合到Ringe（2002）的词汇数据中。为了模拟时空速率异质性，我们在模型中加入了一个突变过程。当一种语言经历一场灾难时，许多特征同时发生变化。我们通过MCMC在贝叶斯设置中拟合完整模型。我们使用贝叶斯因子来验证我们的拟合，以测试已知的年龄限制。我们拒绝了30个历史证明的限制中的3个。我们的主要结果是原始印欧人年龄的一个单模型后验分布，中心在8400年BP，95%HPD等于7100-9800年BP。
英文摘要：
Nicholls and Gray (2008) describe a phylogenetic model for trait data. They use their model to estimate branching times on Indo-European language trees from lexical data. Alekseyenko et al. (2008) extended the model and give applications in genetics. In this paper we extend the inference to handle data missing at random. When trait data are gathered, traits are thinned in a way that depends on both the trait and missing-data content. Nicholls and Gray (2008) treat missing records as absent traits. Hittite has 12% missing trait records. Its age is poorly predicted in their cross-validation. Our prediction is consistent with the historical record. Nicholls and Gray (2008) dropped seven languages with too much missing data. We fit all twenty four languages in the lexical data of Ringe (2002). In order to model spatial-temporal rate heterogeneity we add a catastrophe process to the model. When a language passes through a catastrophe, many traits change at the same time. We fit the full model in a Bayesian setting, via MCMC. We validate our fit using Bayes factors to test known age constraints. We reject three of thirty historically attested constraints. Our main result is a unimodel posterior distribution for the age of Proto-Indo-European centered at 8400 years BP with 95% HPD equal 7100-9800 years BP.
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