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Sampling from complicated and unknown distributions

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  • Cho, Wendy K. Tam
  • Liu, Yan Y.

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.

Suggested Citation

  • Cho, Wendy K. Tam & Liu, Yan Y., 2018. "Sampling from complicated and unknown distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 170-178.
    • Handle: RePEc:eee:phsmap:v:506:y:2018:i:c:p:170-178
    DOI: 10.1016/j.physa.2018.03.096
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    References listed on IDEAS

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    1. M Keane, 1975. "The Size of the Region-Building Problem," Environment and Planning A, , vol. 7(5), pages 575-577, August.
    2. Chen, Jowei & Rodden, Jonathan, 2013. "Unintentional Gerrymandering: Political Geography and Electoral Bias in Legislatures," Quarterly Journal of Political Science, now publishers, vol. 8(3), pages 239-269, June.
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    Cited by:

    1. Adler, William T. & Wang, Samuel S.-H., 2019. "Response to Cho and Liu, “Sampling from complicated and unknown distributions: Monte Carlo and Markov chain Monte Carlo methods for redistricting”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 591-593.
    2. F. Azizpour & F. Qaderi, 2020. "Optimization, modeling and uncertainty investigation of phenolic wastewater treatment by photocatalytic process in cascade reactor," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 22(7), pages 6315-6342, October.

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