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 |
|---|---|
| Pages (from-to) | 170-178 |
| Number of pages | 9 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 506 |
| DOIs | |
| State | Published - Sep 15 2018 |
| Externally published | Yes |
Funding
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.
Keywords
- Markov Chain Monte Carlo
- Monte Carlo simulation
- Redistricting