  In this paper we propose Hit and Run (HAR) sampling from a tropically convex
set. The key ingredient of HAR sampling from a tropically convex set is
sampling uniformly from a tropical line segment over the tropical projective
torus, which runs linearly in its computational time complexity. We show that
this HAR sampling method samples uniformly from a tropical polytope which is
the smallest tropical convex set of finitely many vertices. Finally, we apply
this novel method to any given distribution using Metropolis-Hasting filtering
over a tropical polytope.
