We introduce a nonparametric model for time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and observations arise via exchangeable sampling. Applications include social and genetic data where only aggregate clustering summaries are observed. To address the intractable likelihood, we develop a tractable inferential framework that avoids label enumeration and direct simulation of the latent state. We exploit a duality between the diffusion and a pure-death process on partitions, together with coagulation operators that encode the effect of new data. These yield closed-form, recursive updates for forward and backward inference. We compute exact posterior distributions of the latent state at arbitrary times and predictive distributions of future or interpolated partitions. This enables online and offline inference and forecasting with full uncertainty quantification, bypassing MCMC and sequential Monte Carlo. Compared to particle filtering, our method achieves higher accuracy, lower variance, and substantial computational gains. We illustrate the methodology with synthetic experiments and a social network application, recovering interpretable patterns in time-varying heterozygosity.

翻译：本文针对由无标签划分构成的离散时间数据，提出一种用于时变未观测概率分布的非参数模型。潜在过程遵循两参数泊松-狄利克雷扩散，观测值通过可交换抽样生成。该模型适用于仅能观测到聚类汇总统计的社会学与遗传学数据。为解决似然函数难以处理的问题，我们发展了一种可操作的推断框架，避免标签枚举与潜在状态直接模拟。研究利用该扩散与划分纯灭过程之间的对偶性，结合编码新数据效应的凝聚算子，可推导出前向与后向推断的闭合递归更新公式。我们可计算任意时刻潜在状态的精确后验分布，以及未来或插值划分的预测分布。该方法无需马尔可夫链蒙特卡洛与序贯蒙特卡洛，即可实现全不确定性量化的在线与离线推断及预测。与粒子滤波相比，本方法具有更高精度、更低方差及显著计算效率提升。通过合成实验与社交网络应用案例，我们验证了该方法在恢复时变异质性的可解释模式方面的有效性。