Separate Exchangeability as Modeling Principle in Bayesian Nonparametrics
This paper addresses the underutilization of separate exchangeability in Bayesian nonparametric (BNP) modeling, noting that existing partially exchangeable models—such as nested Dirichlet process variants—often neglect multidimensional experimental structures (e.g., matrix-valued data, multiple treatment groups), leading to misalignment between prior specification and experimental design. To resolve this, the paper introduces the first systematic BNP framework grounded in separate exchangeability, proposing two novel models: nested random partitioning and ANOVA-type dependent Dirichlet processes (ANOVA-DDP). Both explicitly encode hierarchical experimental structure, ensuring theoretical consistency between prior construction and statistical inference. Empirical evaluation on real-world datasets demonstrates substantial improvements in regression prediction accuracy and clustering interpretability. The proposed framework establishes the first BNP paradigm that simultaneously satisfies rigorous theoretical foundations and practical applicability for complex experimental designs.