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We address in this paper a new approach for fitting spatiotemporal modelswith application in disease mapping using the interaction types 1,2,3, and 4.When we account for the spatiotemporal interactions in disease-mapping models,inference becomes more useful in revealing unknown patterns in the data.However, when the number of locations and/or the number of time points islarge, the inference gets computationally challenging due to the high number ofrequired constraints necessary for inference, and this holds for variousinference architectures including Markov chain Monte Carlo (MCMC) andIntegrated Nested Laplace Approximations (INLA). We re-formulate INLA approachbased on dense matrices to fit the intrinsic spatiotemporal models with thefour interaction types and account for the sum-to-zero constraints, and discusshow the new approach can be implemented in a high-performance computingframework. The computing time using the new approach does not depend on thenumber of constraints and can reach a 40-fold faster speed compared to INLA inrealistic scenarios. This approach is verified by a simulation study and a realdata application, and it is implemented in the R package INLAPLUS and thePython header function: inla1234().

Approximate Bayesian Inference for the Interaction Types 1, 2, 3 and 4 with Application in Disease Mapping