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：本文针对离散时间数据（由未标记的划分组成）提出了一种用于时变未观测概率分布的非参数模型。潜在过程是一个双参数泊松-狄利克雷扩散，观测数据通过可交换抽样产生。该模型适用于仅能观测到聚合聚类摘要的社会与遗传数据领域。为解决似然函数难以处理的问题，我们开发了一个可处理的推断框架，避免了标记枚举和潜在状态的直接模拟。我们利用了扩散过程与划分上的纯死亡过程之间的对偶性，以及编码新数据影响的凝聚算子。这些工具产生了用于前向与后向推断的闭式递归更新。我们计算了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。该方法实现了具备完全不确定性量化的在线与离线推断及预测，绕过了MCMC和序列蒙特卡罗方法。与粒子滤波相比，我们的方法获得了更高的精度、更低的方差和显著的计算效率提升。我们通过合成实验和社交网络应用展示了该方法，成功恢复了时变杂合性中可解释的模式。