A Robust Probabilistic Framework for Handling Missing and Noisy Data in Empirical Research

Abstract

Missing and noisy data remain major threats to the validity, reliability, and interpretability of empirical research. Incomplete observations, measurement error, unstable records, and contaminated predictors can distort parameter estimates, weaken predictive performance, and produce misleading conclusions. This study develops and tests a robust probabilistic framework for handling missing and noisy data in empirical research. The framework integrates data-quality diagnosis, probabilistic recovery, likelihood-based estimation, robust probability weighting, and uncertainty reporting. The empirical design uses two public real-world datasets as separate validation cases: 4,240 healthcare records for ten-year coronary heart disease prediction and 7,043 business records for customer churn prediction. We first profiled native missingness, then introduced controlled missingness and noise scenarios into the training data while keeping the test data fixed. We compared complete-case analysis, median/mode probability modeling, iterative likelihood imputation, and robust probability modeling using the area under the receiver operating characteristic curve (ROC-AUC), accuracy, F1 score, Brier score, log loss, predictive entropy, and retained training sample size. The results show that complete-case analysis becomes unstable when data degradation increases, retaining only 11 healthcare training records under the strongest degradation setting and failing to provide a stable complete-case model in the corresponding business scenario. Probability-based approaches preserved discrimination as missingness and noise increased, with ROC-AUC values remaining around 0.70 in the healthcare case and around 0.83 in the business case. The robust probability model produced the strongest calibration evidence in the business robustness case, while iterative likelihood modeling improved probability quality in the healthcare case under moderate and severe degradation. The study contributes an empirical framework for uncertainty-aware analysis of imperfect datasets.