In this paper, we construct an approximation to the Pitman–Yor process by truncating its two-parameter Poisson–Dirichlet representation. The truncation is based on a decreasing sequence of random weights, thus having a lower approximation error compared to the popular truncated stick-breaking process. We develop an exact simulation algorithm to sample from the approximation process and provide an alternative MCMC algorithm for the parameter regime where the exact simulation algorithm becomes slow. The effectiveness of the simulation algorithms is demonstrated by the estimation of the functionals of a Pitman–Yor process. Then we adapt the approximation process into a Pitman–Yor process mixture model and devise a blocked Gibbs sampler for posterior inference.

中文翻译：

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Pitman-Yor 过程分层模型的截断二参数 Poisson-Dirichlet 近似

在本文中，我们通过截断 Pitman-Yor 过程的两参数 Poisson-Dirichlet 表示来构造其近似值。截断基于随机权重的递减序列，因此与流行的截断断棍过程相比具有较低的近似误差。我们开发了一种精确模拟算法来从近似过程中进行采样，并为精确模拟算法变慢的参数范围提供替代 MCMC 算法。模拟算法的有效性通过 Pitman-Yor 过程泛函的估计得到证明。然后，我们将近似过程改编为 Pitman-Yor 过程混合模型，并设计用于后验推理的阻塞吉布斯采样器。