  The pooling of prior opinions is an important area of research and has been
for a number of decades. The idea is to obtain a single belief probability
distribution from a set of expert opinion belief distributions. The paper
proposes a new way to provide a resultant prior opinion based on a minimization
of information principle. This is done in the square-root density space, which
is identified with the positive orthant of Hilbert unit sphere of
differentiable functions. It can be shown that the optimal prior is easily
identified as an extrinsic mean in the sphere. For distributions belonging to
the exponential family, the necessary calculations are exact, and so can be
directly applied. The idea can also be adopted for any neighbourhood of a
chosen base prior and spanned by a finite set of ``contaminating" directions.
