Bayesian nonparametric modeling of dynamic pollution clusters through an autoregressive logistic-beta Stirling-gamma process

Fine suspended particulates (FSP), commonly known as PM2.5, are among the most harmful air pollutants, posing serious risks to population health and environmental integrity. As such, accurately identifying latent clusters of FSP is essential for effective air quality and public health management. This task, however, is notably nontrivial as FSP clusters may depend on various regional and temporal factors, which should be incorporated in the modeling process. Thus, we capitalize on Bayesian nonparametric dynamic clustering ideas, in which clustering structures may be influenced by complex dependencies. Existing implementations of dynamic clustering, however, rely on copula-based dependent Dirichlet processes (DPs), presenting considerable computational challenges for real-world deployment. With this in mind, we propose a more efficient alternative for dynamic clustering by incorporating the novel ideas of logistic-beta dependent DPs. We also adopt a Stirling-gamma prior, a novel distribution family, on the concentration parameter of our underlying DP, easing the process of incorporating prior knowledge into the model. Efficient computational strategies for posterior inference are also presented. We apply our proposed method to identify dynamic FSP clusters across Chile and demonstrate its superior performance over existing approaches.