Slice sampling is a standard Monte Carlo technique for Dirichlet process (DP)-based models, widely used in posterior simulation. However, formal assessments of the scalability of posterior slice samplers have remained largely unexplored, primarily because the computational cost of a slice-sampling iteration is random and potentially unbounded. In this work, we obtain high-probability bounds on the computational complexity of DP slice samplers. Our main results show that, uniformly across posterior cluster-growth regimes, the overhead induced by slice variables, relatively to the number of clusters supported by the posterior, is $O_{\mathbb P}(\log n)$. As a consequence, even in worst-case configurations, superlinear blow-ups in per-iteration computational cost occur with vanishing probability. Our analysis applies broadly to DP-based models without any likelihood-specific assumptions, still providing complexity guarantees for posterior sampling on arbitrary datasets. These results establish a theoretical foundation for assessing the practical scalability of slice sampling in DP-based models.

翻译：切片采样是基于Dirichlet过程（DP）模型的标准蒙特卡洛技术，广泛应用于后验模拟。然而，对后验切片采样器可扩展性的正式评估仍鲜有探索，主要因为切片采样迭代的计算成本是随机的且可能无界。本文得到了DP切片采样器计算复杂性的高概率界。主要结果表明，在后验聚类增长机制中，切片变量相对于后验支持的聚类数所产生的开销统一为$O_{\mathbb P}(\log n)$。因此，即使在最坏配置下，每次迭代计算成本的超线性激增出现的概率趋近于零。我们的分析广泛适用于基于DP的模型，无需任何似然特定假设，仍能为任意数据集上的后验采样提供复杂性保证。这些结果为评估基于DP模型中切片采样的实际可扩展性奠定了理论基础。