  We go through the process of crafting a robust and numerically stable online
algorithm for the computation of the Watanabe-Akaike information criteria
(WAIC). We implement this algorithm in the NIMBLE software. The implementation
is performed in an online manner and does not require the storage in memory of
the complete samples from the posterior distribution. This algorithm allows the
user to specify a specific form of the predictive density to be used in the
computation of WAIC, in order to cater to specific prediction goals. We then
comment and explore via simulations the use of different forms of the
predictive density in the context of different predictive goals. We find that
when using marginalized predictive densities, WAIC is sensitive to the grouping
of the observations into a joint density.
