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Separating Effect From Significance in Markov Chain Tests

Author

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  • Maria Chikina
  • Alan Frieze
  • Jonathan C. Mattingly
  • Wesley Pegden

Abstract

We give qualitative and quantitative improvements to theorems which enable significance testing in Markov chains, with a particular eye toward the goal of enabling strong, interpretable, and statistically rigorous claims of political gerrymandering. Our results can be used to demonstrate at a desired significance level that a given Markov chain state (e.g., a districting) is extremely unusual (rather than just atypical) with respect to the fragility of its characteristics in the chain. We also provide theorems specialized to leverage quantitative improvements when there is a product structure in the underlying probability space, as can occur due to geographical constraints on districtings.

Suggested Citation

  • Maria Chikina & Alan Frieze & Jonathan C. Mattingly & Wesley Pegden, 2020. "Separating Effect From Significance in Markov Chain Tests," Statistics and Public Policy, Taylor & Francis Journals, vol. 7(1), pages 101-114, January.
    • Handle: RePEc:taf:usppxx:v:7:y:2020:i:1:p:101-114
    DOI: 10.1080/2330443X.2020.1806763
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    Cited by:

    1. Sarah Cannon & Ari Goldbloom-Helzner & Varun Gupta & JN Matthews & Bhushan Suwal, 2023. "Voting Rights, Markov Chains, and Optimization by Short Bursts," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-38, March.

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