Modeling of the dependence structure across heterogeneous data is crucial for Bayesian inference since it directly impacts the borrowing of information. Despite the extensive advances over the last two decades, most available proposals allow only for non-negative correlations. We derive a new class of dependent nonparametric priors that can induce correlations of any sign, thus introducing a new and more flexible idea of borrowing of information. This is achieved thanks to a novel concept, which we term hyper-tie, and represents a direct and simple measure of dependence. We investigate prior and posterior distributional properties of the model and develop algorithms to perform posterior inference. Illustrative examples on simulated and real data show that our proposal outperforms alternatives in terms of prediction and clustering.

翻译：异构数据间依赖结构的建模对贝叶斯推断至关重要，因为它直接影响信息的借用。尽管过去二十年取得了大量进展，但现有的大多数方案只能允许非负相关性。我们推导出一类新的依赖非参数先验，能够诱导任意符号的相关性，从而引入一种更灵活的全新信息借用理念。这一创新得益于我们提出的"超连接"概念——一种直接且简洁的依赖度量。我们研究了该模型的先验与后验分布性质，并开发了进行后验推断的算法。在模拟数据和真实数据上的示例表明，我们的方案在预测和聚类方面优于现有替代方法。