  The tools of optimal estimation are applied to the study of subgrid models
for Large-Eddy Simulation of turbulence. The concept of optimal estimator is
introduced and its properties are analyzed in the context of applications to a
priori tests of subgrid models. Attention is focused on the Cook and Riley
model in the case of a scalar field in isotropic turbulence. Using DNS data,
the relevance of the beta assumption is estimated by computing (i) generalized
optimal estimators and (ii) the error brought by this assumption alone. Optimal
estimators are computed for the subgrid variance using various sets of
variables and various techniques (histograms and neural networks). It is shown
that optimal estimators allow a thorough exploration of models. Neural networks
are proved to be relevant and very efficient in this framework, and further
usages are suggested.
