  Many inference problems involving questions of optimality ask for the maximum
or the minimum of a finite set of unknown quantities. This technical report
derives the first two posterior moments of the maximum of two correlated
Gaussian variables and the first two posterior moments of the two generating
variables (corresponding to Gaussian approximations minimizing relative
entropy). It is shown how this can be used to build a heuristic approximation
to the maximum relationship over a finite set of Gaussian variables, allowing
approximate inference by Expectation Propagation on such quantities.
