Random probability measures, together with their constructions, representations, and associated algorithms, play a central role in modern Bayesian inference. A key class is that of proper species sampling processes, which offer a relatively simple yet versatile framework that extends naturally to non-exchangeable settings. We revisit this class from a computational perspective and show that they admit exact finite mixture representations. In particular, we prove that any proper species sampling process can be written, at the prior level, as a finite mixture with a latent truncation variable and reweighted atoms, while preserving its distributional features exactly. These finite formulations can be used as drop-in replacements in Bayesian mixture models, recasting posterior computation in terms of familiar finite-mixture machinery. This yields straightforward MCMC implementations and tractable expressions, while avoiding ad hoc truncations and model-specific constructions. The resulting representation preserves the full generality of the original infinite-dimensional priors while enabling practical gains in algorithm design and implementation.

翻译：随机概率测度及其构造、表示和相关算法在现代贝叶斯推断中起着核心作用。其中关键的一类为正规物种抽样过程，它提供了一个相对简单却功能丰富的框架，并能自然地扩展到非可交换性场景。本文从计算角度重新审视此类过程，证明其具有精确的有限混合表示。具体而言，我们证明了任何正规物种抽样过程在先验层面均可表示为具有潜在截断变量和重加权原子的有限混合形式，同时完全保持其分布特性。这些有限公式可作为贝叶斯混合模型中的即插即用替代方案，将后验计算转化为熟悉的有限混合机制。这产生了直接的MCMC实现和易处理的表达式，同时避免了临时截断和特定模型构造。所得表示在保持原始无限维先验完全通用性的同时，实现了算法设计与实施中的实际效益提升。