  There is a growing interest in the climate community to improve the
prediction of high impact climate events, for instance ENSO
(El-Ni{\~n}o-Southern Oscillation) or extreme events, using a combination of
model and observation data. In this note we explain that, in a dynamical
context, the relevant quantity for predicting a future event is a committor
function. We explain the main mathematical properties of this probabilistic
concept. We compute and discuss the committor function of the Jin and Timmerman
model of El-Ni{\~n}o. Our first conclusion is that one should generically
distinguish between states with either intrinsic predictability or intrinsic
unpredictability. This predictability concept is markedly different from the
deterministic unpredictability arising because of chaotic dynamics and
exponential sensibility to initial conditions. The second aim of this work is
to compare the inference of a committor function from data, either through a
direct approach or through a machine learning approach using neural networks.
We discuss the consequences of this study for future applications to more
complex data sets.
