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

A numerically stable online implementation and exploration of WAIC through variations of the predictive density, using NIMBLE