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

Wendy K.Tam Cho; Yan Y. Liu

doi:10.1016/j.physa.2018.03.096

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

Research output: Contribution to journal › Review 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 language	English (US)
Pages (from-to)	170-178
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	506
DOIs	https://doi.org/10.1016/j.physa.2018.03.096
State	Published - 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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10.1016/j.physa.2018.03.096

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Cho, W. K. T., & Liu, Y. Y. (2018). Sampling from complicated and unknown distributions: Monte Carlo and Markov Chain Monte Carlo methods for redistricting. Physica A: Statistical Mechanics and its Applications, 506, 170-178. https://doi.org/10.1016/j.physa.2018.03.096

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