A Bayesian mixture model for Poisson network autoregression.

Area of Science:

• Statistical modeling
• Network analysis
• Time series analysis

Background:

• Multivariate count time series data are common in various fields, such as epidemiology.
• Traditional models often assume Gaussian errors, which may not be suitable for count data.
• Modeling disease spread on networks requires accounting for spatial relationships and heterogeneous dynamics.

Purpose of the Study:

• To develop a flexible statistical model for count time series data structured on networks.
• To incorporate network structure for sparsity and accommodate heterogeneous node dynamics.
• To cluster nodes exhibiting similar temporal behaviors.

Main Methods:

• Proposed a Bayesian Poisson network autoregression mixture (PNARM) model.
• Combined concepts from Poisson network autoregression, grouped network autoregression, and co-clustering priors.
• Utilized network topology to inform a structural vector autoregression model.

Main Results:

• The PNARM model offers a principled Bayesian approach to network-based count time series.
• The model imposes sparsity through network structure, contrasting with full vector autoregressive models.
• It allows for the clustering of nodes with similar dynamic patterns.

Conclusions:

• The PNARM model provides a robust framework for analyzing count time series on networks.
• It enhances understanding of processes like disease spread by accounting for network structure and heterogeneity.
• This approach facilitates the identification of distinct behavioral clusters within the network.