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Title: A catalogue of graph-based multivariate conditional autoregressive model Authors:  Anna Freni Sterrantino - The Alan Turing (United Kingdom) [presenting]
denis rustand - INSERM U1219 - Bordeaux Population health (France)
Haavard Rue - KAUST (Saudi Arabia)
Abstract: An intuitive approach is presented to define a Multivariate conditional autoregressive model(MCAR) based on graphs and using Kronecker models. The MCAR precision is given as the Kronecker product of the inverse of a correlation matrix and the precision of an Intrinsic Conditional autoregressive model, representing the spatial structure. We frame the MCAR models into the application of multivariate disease mapping and to represent different correlations structures, we have created a catalogue of graphs to model up to four variables (diseases) and introduced the penalized complexity priors as hyper-priors for this parametrization. The penalized complexity priors penalize departures from a model with independent variables and pure overdispersion (base model) compared to a complex model with correlation among diseases and structured spatial variability. The resulted priors are weakly informative and shrink the correlation parameters toward zero. These models find their main application in epidemiology but can be easily extended to other fields of applications.