ABSTRACT
As part of any modeling exercise it is usually of interest to assess how well a given model describes given data. To this end a number of measures have been devised to help in this regard. The first of these is a deviance based measure called the deviance information criterion (DIC). Second the Watanabe-Akaike Information criterion (WAIC) and posterior predictive loss and cross validatory measures. The DIC has been proposed by Spiegelhalter and is widely used in Bayesian modeling. The WAIC can be computed from sampled Markov chain Monte Carlo output and is available automatically within nimble, CARBayes and R-integrated nested Laplace approximation. It is possible to consider a different approach to inference whereby individual observations are compared to the predictive distribution with observations removed. Exceedance probabilities are important when assessing the localized spatial behavior of the model and the assessment of unusual clustering or aggregation of disease.
