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Hit and run sampling from tropically convex sets

Ruriko Yoshida, Keiji Miura and David Barnhill

Vol. 14 (2023), No. 1, 37–69
Abstract

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
Mathematical Subject Classification
Primary: 52B05, 62D99
Milestones
Received: 29 September 2022
Revised: 12 May 2023
Accepted: 14 May 2023
Published: 28 November 2023
Authors
Ruriko Yoshida
Department of Operations Research
Naval Postgraduate School
Monterey, CA
United States
Keiji Miura
Kwansei Gakuin University
Sanda
Hyogo
Japan
David Barnhill
Department of Operations Research
Naval Postgraduate School
Monterey, CA
United States