Bayesian Spatial Functional Data Clustering: Applications in Disease Surveillance.

The ability to accurately cluster contiguous regions with similar disease risk evolution is crucial for effective public health response and resource allocation. In this article, we propose a novel spatial functional clustering model designed for disease risk mapping, utilizing random spanning trees for partitioning and latent Gaussian models for capturing within-cluster structure. This approach enables the identification of spatially contiguous clusters with similar latent functions, representing diverse processes such as trends, seasonality, smooth patterns, and autoregressive behaviors. Our method extends the application of random spanning trees to cases where the response variable belongs to the exponential family, making it suitable for a wide range of real-world scenarios, including non-Gaussian likelihoods. The proposed model addresses the limitations of previous spatial clustering methods by allowing all within-cluster model parameters to be cluster-specific, thus offering greater flexibility. Additionally, we propose a Bayesian inference algorithm that overcomes the computational challenges associated with the reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm by employing composition sampling and the integrated nested Laplace approximation (INLA) to compute the marginal distribution necessary for the acceptance probability. This enhancement improves the mixing and feasibility of Bayesian inference for complex models. We demonstrate the effectiveness of our approach through simulation studies and apply it to real-world disease mapping applications: COVID-19 in the United States of America, and dengue fever in the states of Minas Gerais and São Paulo, Brazil. Our results highlight the model's capability to uncover meaningful spatial patterns and temporal dynamics in disease outbreaks, providing valuable insights for public health decision-making and resource allocation.