Duke Applied Mathematics

Publications [#352640] of Jonathan C. Mattingly

Papers Published

1. Chikina, M; Frieze, A; Mattingly, JC; Pegden, W, Separating Effect From Significance in Markov Chain Tests, Statistics and Public Policy, vol. 7 no. 1 (January, 2020), pp. 101-114 [doi]
   (last updated on 2026/01/20)

   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.