Ecological Archives E095-029-A3

James T. Thorson, Kotaro Ono, Stephan B. Munch. 2014. A Bayesian approach to identifying and compensating for model misspecification in population models. Ecology 95:329–341.

Appendix C. Credible interval estimates.

The conventional and GP models estimate a credible interval for the population growth function f(·). This credible interval is computed by calculating the implied growth function fi(b*) for each Markov chain Monte Carlo sample i from the model posterior at abundance b*, and then calculating quantiles (in this case, 10% and 90%) from this distribution. The credible intervals of the absolute index scenario (Fig. C1 and C3) and the catch data scenario (Fig. C2 and C4) show a similar pattern to the posterior median for each replicate (Fig. 2–4). Specifically, conventional and GP models have very similar credible intervals when the growth function is correctly specified, and this credible interval increases in width as variability increases (this and other credible interval results are confirmed to be qualitatively similar when displaying more credible intervals). The credible interval for the conventional model rarely overlaps the true value given low variability and a misspecified growth function. By contrast, the credible interval for the GP model generally encompasses the true value in this case. As variability increases, the credible interval for both models increases for all growth functions and, in particular, for the catch data scenario, where imprecision in estimating K results in a cloud of credible interval estimates given high variability.


Fig. C1. The ‘true’ population growth function (black line) with eighty-percent credible intervals estimates for the first three replicates of the conventional (blue) and Gaussian process models (red) overlaid for each configuration in the absolute index scenario.