THE GENERALISED INVERSE GAUSSIAN DISTRIBUTION AS A PRIOR FOR DISEASE MAPPING MODELS

In this work we study sensitivity to hyperprior specification of the dispersion parameter in a convolution model widely used in spatial disease mapping, that accounts for both structured (spatial) and unstructured heterogeneity. In the fully Bayesian approach to disease mapping, hyperprior choice sensibly affects inferences. In this work we critically review the most common hyperprior specifications. Moreover we propose a new hyperprior distribution, the Generalised Inverse Gaussian, starting from an idea explored in the estimation of the mean for iid log-Normal observations. In this context it is well known that hyperprior parameters have to be set accurately in order to avoid infinite moments of the posterior distribution. The performances of various hyperprior choices are compared via simulation studies. In particular we investigate the sensitivity of the relative risk estimates.