A one-step-ahead pseudo-DIC for comparison of Bayesian state-space models

In the context of state-space modeling, conventional usage of the deviance information criterion (DIC) evaluates the ability of the model to predict an observation at time t given the underlying state at time t. Motivated by the failure of conventional DIC to clearly choose between competing multivariate nonlinear Bayesian state-space models for coho salmon population dynamics, and the computational challenge of alternatives, this work proposes a one-step-ahead DIC, DICp, where prediction is conditional on the state at the previous time point. Simulations revealed that DICp worked well for choosing between state-space models with different process or observation equations. In contrast, conventional DIC could be grossly misleading, with a strong preference for the wrong model. This can be explained by its failure to account for inflated estimates of process error arising from the model mis-specification. DICp is not based on a true conditional likelihood, but is shown to have interpretation as a pseudo-DIC in which the compensatory behavior of the inflated process errors is eliminated. It can be easily calculated using the DIC monitors within popular BUGS software when the process and observation equations are conjugate. The improved performance of DICp is demonstrated by application to the multi-stage modeling of coho salmon abundance in Lobster Creek, Oregon.