Modeling temporal dependence in a sequence of spatial random partitions driven by spanning tree: an application to mosquito-borne diseases

TL;DR

This paper introduces a Bayesian spatio-temporal clustering model using spanning trees to analyze the evolution of spatial partitions, applied to mosquito-borne disease data in Brazil, demonstrating its effectiveness through real and simulated data.

Contribution

It proposes a novel Bayesian model with spanning trees for correlated temporal spatial partitions, tailored for overdispersed disease count data.

Findings

Model effectively captures temporal evolution of spatial clusters.

Application to dengue data reveals meaningful spatio-temporal patterns.

Model performs well on simulated datasets.

Abstract

Spatially constrained clustering is an important field of research, particularly when it involves changes over time. Partitioning a map is not simple since there is a vast number of possible partitions within the search space. In spatio-temporal clustering, this task becomes even more difficult, as we must consider sequences of partitions. Motivated by these challenges, we introduce a Bayesian model for time-dependent sequences of spatial random partitions by proposing a prior distribution based on product partition models that correlates partitions. Additionally, we employ random spanning trees to facilitate the exploration of the partition search space and to guarantee spatially constrained clustering. This work is motivated by a relevant applied problem: identifying spatial and temporal patterns of mosquito-borne diseases. Given the overdispersion present in this type of data, we introduce a spatio-temporal Poisson mixture model in which mean and dispersion parameters vary according to spatio-temporal covariates. The proposed model is applied to analyze the number of dengue cases reported weekly from 2018 to 2023 in the Southeast region of Brazil. We also evaluate model performance using simulated data. Overall, the proposed model has proven to be a competitive approach for analyzing the temporal evolution of spatial clustering.