A finite population parametric Bayesian bootstrap for quick counts
Carlos E. Rodríguez, Stephen G. Walker, Ramsés H. Mena
The Annals of Applied Statistics · 2025 · Volume 19 · Issue 4
Abstract
The theoretical backdrop to this paper is the finite population Bayesian bootstrap and recent developments on martingale posterior distributions. From these ideas we introduce a novel method for Bayesian parametric finite population inference. The proposed approach, which is model-based and designed to facilitate uncertainty quantification, allows for the estimation of any quantity of interest from the finite population. Specifically, the unobserved part of the finite population is imputed via a predictive model guided by a martingale. The quantity of interest is then computed based on the entire population, encompassing both observed and imputed values. This iterative process is repeated multiple times to capture the uncertainty. The motivation for this proposal stems from the Quick Counts organized by the National Electoral Institute of Mexico. To assess the method, the study utilizes two real-world open datasets: the 2021 Mexican referendum on prosecuting former presidents for corruption and the 2017 State of Mexico governor election voting data. A comparative analysis, including established methods from the literature, approaches based on Bayesian principles, and methods derived from our proposed ideas, is conducted for a comprehensive evaluation.
Keywords
Bayesian analysis; imputation; predictive inference; sampling;
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