Measuring the information content of ensemble predictions in dynamical systems relevant to atmosphere and ocean

In the past two years a new theoretical framework for analyzing predictive information has been developed by the author for geophysical applications. This has been motivated by the very practical issue of determining how predictive utility varies from one prediction to another. The framework relies on entropic information theoretic functionals on probability distribution functions (pdfs). The latter describe the random variables of interest. In practical contexts only an estimate of these functions is possible usually by means of a Monte-Carlo ensemble or sample of predictions which are distributed according to the (unknown) pdf. Obviously this imperfect knowledge of how the random variables are distributed implies a further reduction in the information content of the prediction made. We use Bayesian analysis tools to quantify this loss and discuss the relation to maximum entropy methodologies from mathematical statistics.