Discrete nonparametric priors play a central role in a variety of Bayesian procedures, most notably when used to model latent features as in clustering, mixtures and curve fitting. They are effective and well developed tools, though their infinite-dimensionality is unsuited to several applications. If one confines oneself to a finite-dimensional simplex, there are few nonparametric priors beyond the traditional Dirichlet-multinomial process, which is mainly motivated by conjugacy. Here we introduce an alternative based on the Pitman–Yor process, which ensures greater flexibility while preserving analytical tractability. Urn schemes and posterior characterizations are obtained in closed form, leading to exact sampling methods. In addition, our proposal can be used to accurately approximate the infinite-dimensional Pitman–Yor process, improving over existing truncation-based approaches. An application to convex mixture regression for quantitative risk assessment serves as an illustration of our results and allows comparisons with existing methodologies.

中文翻译：

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用于混合建模的 Pitman-Yor 多项式过程

离散非参数先验在各种贝叶斯程序中发挥着核心作用，尤其是在用于对潜在特征进行建模时，如聚类、混合和曲线拟合。它们是有效且开发良好的工具，尽管它们的无限维度不适用于多种应用。如果将自己局限于有限维单纯形，那么除了传统的 Dirichlet 多项式过程之外，几乎没有非参数先验，这主要是由共轭性驱动的。在这里，我们介绍了一种基于 Pitman-Yor 过程的替代方案，它确保了更大的灵活性，同时保持了分析的易处理性。瓮方案和后验特征以封闭形式获得，从而产生精确的采样方法。此外，我们的提议可用于精确逼近无限维 Pitman-Yor 过程，改进了现有的基于截断的方法。用于定量风险评估的凸混合回归的应用可作为我们结果的说明，并允许与现有方法进行比较。