Non-reversible Markov chain Monte Carlo for sampling of districting maps

Herschlag, Gregory

Mattingly, Jonathan C

Sachs, Matthias

Wyse, Evan

2020-08-27T13:34:02Z

2020-08-27T13:34:02Z

2020-08-27T13:33:58Z

Evaluating the degree of partisan districting (Gerrymandering) in a statistical framework typically requires an ensemble of districting plans which are drawn from a prescribed probability distribution that adheres to a realistic and non-partisan criteria. In this article we introduce novel non-reversible Markov chain Monte-Carlo (MCMC) methods for the sampling of such districting plans which have improved mixing properties in comparison to previously used (reversible) MCMC algorithms. In doing so we extend the current framework for construction of non-reversible Markov chains on discrete sampling spaces by considering a generalization of skew detailed balance. We provide a detailed description of the proposed algorithms and evaluate their performance in numerical experiments.

https://hdl.handle.net/10161/21346

stat.CO

stat.CO

math.PR

60J10, 60J20, 62P99

G.3; G.2

Non-reversible Markov chain Monte Carlo for sampling of districting maps

Journal article

Herschlag, Gregory|0000-0001-5443-6449

Mattingly, Jonathan C|0000-0002-1819-729X

Sachs, Matthias|0000-0002-9003-337X

Trinity College of Arts & Sciences

Mathematics

Duke

Staff