  This paper develops new methodology, together with related theories, for
combining information from independent studies through confidence
distributions. A formal definition of a confidence distribution and its
asymptotic counterpart (i.e., asymptotic confidence distribution) are given and
illustrated in the context of combining information. Two general combination
methods are developed: the first along the lines of combining p-values, with
some notable differences in regard to optimality of Bahadur type efficiency;
the second by multiplying and normalizing confidence densities. The latter
approach is inspired by the common approach of multiplying likelihood functions
for combining parametric information. The paper also develops adaptive
combining methods, with supporting asymptotic theory which should be of
practical interest. The key point of the adaptive development is that the
methods attempt to combine only the correct information, downweighting or
excluding studies containing little or wrong information about the true
parameter of interest. The combination methodologies are illustrated in
simulated and real data examples with a variety of applications.
