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 computational 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–Hastings filtering over a tropical
polytope.
Keywords
hit and run sampling, tropical geometry, Markov chain Monte
Carlo, tropical convexity