  Dynamical modelling lies at the heart of our understanding of physical
systems. Its role in science is deeper than mere operational forecasting, in
that it allows us to evaluate the adequacy of the mathematical structure of our
models. Despite the importance of model parameters, there is no general method
of parameter estimation outside linear systems. A new relatively simple method
of parameter estimation for nonlinear systems is presented, based on variations
in the accuracy of probability forecasts. It is illustrated on the Logistic
Map, the Henon Map and the 12-D Lorenz96 flow, and its ability to outperform
linear least squares in these systems is explored at various noise levels and
sampling rates. As expected, it is more effective when the forecast error
distributions are non-Gaussian. The new method selects parameter values by
minimizing a proper, local skill score for continuous probability forecasts as
a function of the parameter values. This new approach is easier to implement in
practice than alternative nonlinear methods based on the geometry of attractors
or the ability of the model to shadow the observations. New direct measures of
inadequacy in the model, the "Implied Ignorance" and the information deficit
are introduced.
