Separating Effect From Significance in Markov Chain Tests

Maria Chikina, Alan Frieze, Jonathan C. Mattingly and Wesley Pegden

Statistics and Public Policy, 2020, vol. 7, issue 1, 101-114

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.

Date: 2020
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DOI: 10.1080/2330443X.2020.1806763

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