There is a trend in biomedical and public health research towards outcome measures of increasing complexity. This project aims to develop novel statistical methodology for multivariate epidemiological count data. Correlated Gaussian Markov random field models based on a Kronecker product precision matrix will be developed. This framework will provide great flexibility for structured additive regression and will be particularly suitable for longitudinal and space-time data. Algorithmic routines based on both Markov chain Monte Carlo (MCMC) and integrated nested Laplace approximations (INLA) will be developed and compared.