  A collider, where particles are injected to a beam splitter from opposite
sides, has been used for identifying quantum statistics of identical particles.
The collision leads to bunching of the particles for bosons and antibunching
for fermions. In recent experiments, a collider was applied to a fractional
quantum Hall regime hosting Abelian anyons. The observed negative cross
correlation of electrical currents cannot be understood with fermionic
antibunching. Here we predict, based on a conformal field theory and
non-perturbative treatment of non-equilibrium anyon injection, that the
collider provides a tool for direct observation of the braiding statistics of
various Abelian and non-Abelian anyons. Its dominant process is not direct
collision between injected anyons, contrary to common expectation, but braiding
between injected anyons and an anyon excited at the collider. The dependence of
the resulting negative cross correlation on the injection currents
distinguishes non-Abelian SU(2)$_k$ anyons, Ising anyons, and Abelian Laughlin
anyons.
