  The problem of determining a metal's Fermi surface from measurements of
projections of the electron or electron/positron momentum densities, such as
obtained by Compton Scattering or Angular Correlation of Positron Annihilation
Radiation, respectively, is considered in a Bayesian formulation. A consistent
approach is presented and its advantages compared to previous practice is
discussed. A validation of the proposed method on simulated data shows its
systematic accuracy to be very satisfactory and its statistical precision on
modest experimental data to be surprisingly good.
