Separating effect from significance in Markov chain tests
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.
Cite
@article{arxiv.1904.04052,
title = {Separating effect from significance in Markov chain tests},
author = {Maria Chikina and Alan Frieze and Jonathan Mattingly and Wesley Pegden},
journal= {arXiv preprint arXiv:1904.04052},
year = {2019}
}
Comments
title changed. (was: "Practical tests for significance in Markov chains"). 22 pages