论文标题
基于投影的Pólya树的定向数据的多元和回归模型
Multivariate and regression models for directional data based on projected Pólya trees
论文作者
论文摘要
事实证明，预计的分布在研究循环和定向数据的研究中很有用。尽管任何多元分布都可以用于生成投影模型，但这些分布通常是参数。在本文中，我们考虑了$ r^k $上的多元pólya树，然后将其投影到hypersphere $ s^k $上，以定义用于方向数据的新贝叶斯非参数模型。我们研究了所提出的模型的特性，尤其是集中于某些方向的隐含条件分布，以定义方向性回归模型。我们还定义了具有Pólya树误差的多元线性回归模型，并将其投影以定义线性回归模型。我们获得了所有模型的后验特征，并通过模拟和真实数据集显示其性能。
Projected distributions have proved to be useful in the study of circular and directional data. Although any multivariate distribution can be used to produce a projected model, these distributions are typically parametric. In this article we consider a multivariate Pólya tree on $R^k$ and project it to the unit hypersphere $S^k$ to define a new Bayesian nonparametric model for directional data. We study the properties of the proposed model and in particular, concentrate on the implied conditional distributions of some directions given the others to define a directional-directional regression model. We also define a multivariate linear regression model with Pólya tree error and project it to define a linear-directional regression model. We obtain the posterior characterisation of all models and show their performance with simulated and real datasets.
