TY - JOUR
T1 - Sampling from complicated and unknown distributions
T2 - Monte Carlo and Markov Chain Monte Carlo methods for redistricting
AU - Cho, Wendy K.Tam
AU - Liu, Yan Y.
N1 - Funding Information:
This research has been funded in part by the National Science Foundation, United States (Grant No. SES-1725418/1728902 ) and the Guggenheim Foundation, United States , as well as multiple computing allocation grants on the Blue Waters sustained-petascale computing resources, which is supported by the NSF, United States (Grants OCI-0725070 and ACI-1238993 ) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and the National Center for Supercomputing Applications.
Publisher Copyright:
© 2018 Elsevier B.V.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/9/15
Y1 - 2018/9/15
N2 - 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.
AB - 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.
KW - Markov Chain Monte Carlo
KW - Monte Carlo simulation
KW - Redistricting
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U2 - 10.1016/j.physa.2018.03.096
DO - 10.1016/j.physa.2018.03.096
M3 - Review article
AN - SCOPUS:85046170598
VL - 506
SP - 170
EP - 178
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
ER -