What is the value of an observable between pre- and postselection?

Hall's recent derivation of an exact uncertainty relation [Phys. Rev. A 64 (2001) 052103] is revisited. It is found that the Bayes estimator of an observable between pre- and postselection equals the real part of the weak value. The quadratic loss function equals the expectation of the squared imaginary part of the weak value. (C) 2004 Elsevier B.V. All rights reserved.