  Critical transitions in multistable systems have been discussed as models for
a variety of phenomena ranging from the extinctions of species to
socio-economic changes and climate transitions between ice-ages and warm-ages.
From bifurcation theory we can expect certain critical transitions to be
preceded by a decreased recovery from external perturbations. The consequences
of this critical slowing down have been observed as an increase in variance and
autocorrelation prior to the transition. However especially in the presence of
noise it is not clear, whether these changes in observation variables are
statistically relevant such that they could be used as indicators for critical
transitions. In this contribution we investigate the predictability of critical
transitions in conceptual models. We study the quadratic integrate-and-fire
model and the van der Pol model, under the influence of external noise. We
focus especially on the statistical analysis of the success of predictions and
the overall predictability of the system. The performance of different
indicator variables turns out to be dependent on the specific model under study
and the conditions of accessing it. Furthermore, we study the influence of the
magnitude of transitions on the predictive performance.
