Lay summary
The goal of this project is to develop novel statistical methods for the analysis of dependent multivariate count data from epidemiology. There are two main areas of research. First, new methodology for structured Poisson regression models will be developed. This framework includes important special cases such as age-period-cohort models for count data stratified by age group and calendar time or spatial and spatio-temporal models from geographical epidemiology. Modern inference techniques, in particular efficient Markov chain Monte Carlo(MCMC) algorithms based on auxiliary variables and numerical methods based on integrated nested Laplace approximations will be considered.The methodology will be applied to multivariate mortality data obtained from the Swiss National Cohort.Secondly, statistical methods for the analysis of multivariate infectious disease surveillance data will be advanced further. Random effects will be incorporated in the multivariate models developed so far. This will enable the analysis of high-dimensional multivariate time series of counts with heterogeneity in the model coefficients.The predictive properties of the models proposed will be validated based on proper scoring rules and related techniques. Finally, a regression-based approach to incorporate possible dependence of infectiveness parameters on covariates will be considered.