A variance-based framework for robust variable selection under correlated inputs and unobserved factors

Calibration of sensors in partially observed and correlated environments raises fundamental challenges for variable selection and model interpretation. When observations are noisy and influenced by unmeasured factors, classical selection criteria based on regression coefficients, crossvalidation errors, or sensitivity indices may fail to identify the variables that most effectively reduce uncertainty in the target quantity. This paper introduces a probabilistic framework for variable selection based on variance reduction and prediction stability. The proposed approach relies on the systematic evaluation of models built from different subsets of observed variables and on a criterion that minimizes conditional prediction variance under a parsimony constraint. This criterion naturally penalizes spurious correlations and distinguishes variables that contribute to uncertainty reduction from those that merely compensate for missing information. The framework is illustrated through analytical examples and numerical experiments on simulated data, which highlight its robustness to noise and unmeasured confounders. Although motivated by calibration problems in environmental sensing, the proposed methodology is general and applicable to a wide range of regression and inference tasks involving correlated inputs and unobserved factors.