Sampling from complicated and unknown distributions: Monte Carlo and Markov Chain Monte Carlo methods for redistricting

Wendy K.Tam Cho, Yan Y. Liu

Research output: Contribution to journalReview article

Abstract

Sampling from complicated and unknown distributions has wide-ranging applications. Standard Monte Carlo techniques are designed for known distributions and are difficult to adapt when the distribution is unknown. Markov Chain Monte Carlo (MCMC) techniques are designed for unknown distributions, but when the underlying state space is complex and not continuous, the application of MCMC becomes challenging and no longer straightforward. Both of these techniques have been proposed for the astronomically large redistricting application that is characterized by an extremely complex and idiosyncratic state space. We explore the theoretic applicability of these methods and evaluate their empirical performance.

Original languageEnglish (US)
Pages (from-to)170-178
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Volume506
DOIs
StatePublished - Sep 15 2018

Keywords

  • Markov Chain Monte Carlo
  • Monte Carlo simulation
  • Redistricting

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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