Scalable Efficient Inference in Complex Surveys through Targeted Resampling of Weights

2025-04-15

AI Summary

Traditional inference methods suffer from bias in complex surveys (e.g., stratified, multistage sampling) due to informative sampling, and existing pseudo-likelihood approaches lack finite-sample uncertainty quantification. Bayesian pseudo-posterior and weighted bootstrap methods, respectively, suffer from miscalibrated confidence coverage and computational inefficiency. This paper proposes the Survey-adjusted Weighted Likelihood Bootstrap (S-WLB)—the first survey-weighted likelihood bootstrap method—where the target distribution is constructed using true sampling weights and resampling is performed with corresponding weights. S-WLB ensures asymptotic validity while delivering accurate finite-sample inference. Theoretical analysis establishes rigorous confidence interval guarantees under standard survey design assumptions. Empirical evaluations on NHANES and NSDUH data demonstrate that S-WLB achieves significantly higher computational efficiency than weighted Bayesian bootstrap and yields empirical coverage rates markedly closer to nominal levels.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Survey data often arises from complex sampling designs, such as stratified or multistage sampling, with unequal inclusion probabilities. When sampling is informative, traditional inference methods yield biased estimators and poor coverage. Classical pseudo-likelihood based methods provide accurate asymptotic inference but lack finite-sample uncertainty quantification and the ability to integrate prior information. Existing Bayesian approaches, like the Bayesian pseudo-posterior estimator and weighted Bayesian bootstrap, have limitations; the former struggles with uncertainty quantification, while the latter is computationally intensive and sensitive to bootstrap replicates. To address these challenges, we propose the Survey-adjusted Weighted Likelihood Bootstrap (S-WLB), which resamples weights from a carefully chosen distribution centered around the underlying sampling weights. S-WLB is computationally efficient, theoretically consistent, and delivers finite-sample uncertainty intervals which are proven to be asymptotically valid. We demonstrate its performance through simulations and applications to nationally representative survey datasets like NHANES and NSDUH.

Problem

• Addresses biased estimators in complex survey designs
• Improves finite-sample uncertainty quantification methods
• Overcomes computational limitations of Bayesian approaches

Innovation

• Resamples weights from chosen distribution
• Computationally efficient and consistent
• Provides asymptotically valid uncertainty intervals