Does "model-free" forecasting really outperform the "true" model? A reply to Perretti et al

Estimating population models from uncertain observations is an important problem in ecology. Perretti et al. observed that standard Bayesian state-space solutions to this problem may provide biased parameter estimates when the underlying dynamics are chaotic. Consequently, forecasts based on these estimates showed poor predictive accuracy compared to simple "model-free" methods, which lead Perretti et al. to conclude that "Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data". However, a simple modification of the statistical methods also suffices to remove the bias and reverse their results.