Adaptive Gaussian Markov random field spatiotemporal models for infectious disease mapping and forecasting.

Recent disease mapping literature presents adaptively parameterized spatiotemporal (ST) autoregressive (AR) or conditional autoregressive (CAR) models for Bayesian prediction of COVID-19 infection risks. These models were motivated to capture complex spatiotemporal dynamics and heterogeneities of infection risks. In the present paper, we synthesize, generalize, and unify the ST AR and CAR model constructions for models augmented by adaptive Gaussian Markov random fields, with an emphasis on disease forecasting. A general convolution construction is presented, with illustrative models motivated to (i) characterize local risk dependencies and influences over both spatial and temporal dimensions, (ii) model risk heterogeneities and discontinuities, and (iii) predict and forecast areal-level disease risks and occurrences. The broadened constructions allow rich options of intuitive parameterization for disease mapping and spatial regression. Illustrative parameterizations are presented for Bayesian hierarchical models of Poisson, zero-inflated Poisson, and Bernoulli data models, respectively. They are also discussed in the context of quantifying time-varying or time-invariant effects of (omitted) covariates, with application to prediction and forecasting areal-level COVID-19 infection occurrences and probabilities of zero-infection. The model constructions presented herein have much wider scope in offering a flexible framework for modelling complex spatiotemporal data and for estimation, learning, and forecasting purposes.