Hierarchical normalized discrete random measures identify a general class of priors that is suited to flexibly learn how the distribution of a response variable changes across groups of observations. A special case widely used in practice is the hierarchical Dirichlet process. Although current theory on hierarchies of nonparametric priors yields all relevant tools for drawing posterior inference, their implementation comes at a high computational cost. We fill this gap by proposing an approximation for a general class of hierarchical processes, which leads to an efficient conditional Gibbs sampling algorithm. The key idea consists of a deterministic truncation of the underlying random probability measures leading to a finite dimensional approximation of the original prior law. We provide both empirical and theoretical support for such a procedure.

分层归一化的离散随机度量确定了一般先验类别，该先验类别适合于灵活地学习响应变量在各个观察组之间的分布如何变化。在实践中广泛使用的特殊情况是分层Dirichlet过程。尽管当前关于非参数先验层次的理论提供了所有用于得出后验推断的相关工具，但是其实现却需要很高的计算成本。我们通过为一类通用的分层过程提出一个近似值来填补这一空白，这导致了一种有效的条件式Gibbs采样算法。关键思想包括对基础随机概率度量的确定性截断，从而导致原始先验定律的有限维近似。我们为这种程序提供了经验和理论支持。