Separating Effect From Significance in Markov Chain Tests. Issue 1 (1st January 2020)

• Record Type: Journal Article
• Authors: Chikina, Maria; Frieze, Alan; Mattingly, Jonathan C.; Pegden, Wesley
• Is Part Of: Statistics and public policy. Volume 7:Issue 1(2020)
• Page Start: 101
• Page End: 114
• Publication Date: 2020-01-01
• Subjects: Gerrymandering -- Markov chain -- Outlier; Policy sciences -- Methodology -- Periodicals; Social sciences -- Statistical methods -- Periodicals; Medical statistics -- Methodology -- Periodicals; Statistics -- Periodicals; Medical statistics -- Methodology; Policy sciences -- Methodology; Social sciences -- Statistical methods; Statistics; Periodicals; 320.60727
• DOI: 10.1080/2330443X.2020.1806763
• Languages: English
• ISSNs: 2330-443X

Abstract

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.