We introduce a nonparametric model for inferring 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：本文提出一种非参数模型，用于从未标记分区的离散时间数据中推断随时间演变的未观测概率分布。潜在过程是双参数泊松-狄利克雷扩散，观测值通过可交换抽样生成。应用场景包括仅能获取聚合聚类摘要的社会与遗传数据。为处理难解似然函数，我们开发了一个无需标签枚举和潜在状态直接仿真的可推断框架。利用扩散与分区上的纯消亡过程之间的对偶性，结合编码新数据效应的凝聚算子，推导出前向与后向推断的封闭形式递归更新。可计算任意时刻潜在状态的精确后验分布，以及未来或插值分区的预测分布。该方法在完全量化不确定性的前提下实现在线与离线推断及预测，无需马尔可夫链蒙特卡洛或序贯蒙特卡洛方法。与粒子滤波相比，本方法具有更高精度、更低方差及显著的计算优势。通过合成实验和社交网络应用案例，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。