Optimal prediction (OP) methods compensate for a lack of resolution in the
numerical solution of complex problems through the use of an invariant measure
as a prior measure in the Bayesian sense. In first-order OP, unresolved
information is approximated by its conditional expectation with respect to the
invariant measure. In higher-order OP, unresolved information is approximated
by a stochastic estimator, leading to a system of random or stochastic
differential equations.
We explain the ideas through a simple example, and then apply them to the
solution of Averaged Euler equations in two space dimensions.Comment: 13 pages, 2 figure
