4. Discussion
4.1. Why using parametric forecasting?
This study aimed at highlighting two key advantages of parametric
approaches to forecasting. First, Bayesian model checking procedures
are powerful tools to asses the misfit of a model calibrated on real
data. These tools enable to identify cases in which our modeled
understanding of an ecological system is too crude to make reliable
predictions. In such cases, modifications of the model should be
sought, before any reliable predictions can be made. By re-examining
the toy example of the theta-logistic model proposed by Perretti et al.
(2013c), it was shown that a simple model checking procedure was
sufficient, provided that observation noise was not too large, to
distinguish cases in which model misfit was large and parametric
forecasting poor from cases in which model misfit was not evidenced
and parametric forecasting was reasonably good (Figs. 2 and 4). For
real case studies, it is difficult to advise the use of a particular
threshold below which a model should be considered to fail at fitting
the data. Such procedures enable to detect model misfit, when a
posterior predictive p-Value is clearly lower than the distribution of
posterior predictive p-Values obtained on data generated with the
parametric model (e.g., Fig. 2A and B, for θ values equal to or larger
than 1.5). In such cases, they will indicate particular patterns in the
data that the model may not reproduce accurately, and therefore
guide model improvements. Model checking procedures also confirm
a good model fit to data, when the posterior predictive p-Value is
within the central range of the reference distribution. In less clear-cut
cases, model checking still provides ecologists with a quantification of
the model fit quality