  Some models describing unconventional fractional quantum Hall states predict
quasiparticles that obey nonabelian quantum statistics. The most prominent
example is the Moore-Read model for the $\nu=5/2$ state, in which the ground
state is a superconductor of composite fermions, and the charged excitations
are vortices in that superconductor. In this paper we develop a physical
picture of the nonabelian statistics of these vortices. Considering first the
positions of the vortices as fixed, we define a set of single-particle states
at and near the core of each vortex, and employ general properties of the
corresponding Bogolubov-deGennes equations to write the ground states in the
Fock space defined by these single-particle states. We find all ground states
to be entangled superpositions of all possible occupations of the
single-particle states near the vortex cores, in which the probability for all
occupations is equal, and the relative phases vary from one ground state to
another. Then, we examine the evolution of the ground states as the positions
of the vortices are braided. We find that as vortices move, they accumulate a
geometric phase that depends on the occupations of the single-particle states
near the cores of other vortices. Thus, braiding of vortices changes the
relative phase between different components of a superposition, in which the
occupations of the single-particle states differ, and hence transform the
system from one ground state to another. These transformations are the source
of the nonabelian statistics. Finally, by exploring a "self-similar" form of
the many-body wave functions of the ground states, we show the equivalence of
our picture and pictures derived previously, in which vortex braiding seemingly
affects the occupations of states in the cores of the vortices.
