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We discuss the problem of softening a hard quadratic bound to generate a personal prior probability distribution. The quadratic bound requires the model vector to live within a hyperspherical volume. Prior information suggests we may work in a finite-dimensional space, thus avoiding the known difficulties associated with infinite-dimensional spaces, and that values of the Euclidean 2-norm within the volume are uniformly distributed. The application is to the estimation of the magnetic field at the core-mantle boundary. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]