A Bayes-Factor-Guided Approach to Post-Double Selection with Bootstrapped Multiple Imputation
Johannes Bleher, Claudia Tarantola
TLDR
This paper introduces a Bayes-factor-guided sequential evidence aggregation method for robust variable selection in bootstrapped and imputed datasets.
Key contributions
- Proposes a sequential evidence aggregation procedure for robust variable selection in perturbed datasets.
- Models variable detection as Bernoulli trials, accumulating evidence via a likelihood-ratio process with Bayes-factor interpretation.
- Offers a variable inclusion criterion and an adaptive stopping rule, eliminating the need to pre-fix iteration counts.
- Validated through extensive Monte Carlo studies and an empirical illustration, showing superior performance.
Why it matters
This method addresses a critical challenge in statistical modeling by providing a more stable and efficient way to select variables from complex, perturbed datasets. It improves model robustness and interpretability, which is crucial for reliable inference in fields using bootstrapping and multiple imputation.
Original Abstract
When variable selection methods are applied to bootstrapped and multiply imputed datasets, the set of selected variables typically varies across iterations. Aggregating results via the union rule can lead to overly dense models. We propose a sequential evidence aggregation procedure that models detection outcomes across perturbation iterations as Bernoulli trials and accumulates evidence for variable relevance through a likelihood-ratio process admitting an approximate Bayes-factor interpretation. The procedure provides both a variable inclusion criterion and a stopping rule that eliminates the need to fix the number of bootstrap-imputation iterations ex ante. A Monte Carlo study across 126 scenarios and an empirical illustration demonstrate the method's performance relative to existing aggregation approaches.
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