Bayes-Factor-Guided Post-Double Selection with Bootstrapped Multiple Imputation
Aggregates variable-selection evidence across bootstrap and multiple-imputation runs with Bayes-factor-style stopping and inclusion rules.
This project develops a sequential evidence aggregation layer for post-double selection when the data are repeatedly perturbed through bootstrap resampling and multiple imputation. The problem is that the selected adjustment set usually changes across bootstrap-imputation iterations. Simple union rules can become too dense, while fixed frequency thresholds can discard variables that carry persistent but weaker evidence.
Together with Claudia Tarantola, I model variable-detection outcomes across perturbation runs as evidence about covariate relevance. A likelihood-ratio process with an approximate Bayes-factor interpretation provides both a variable inclusion rule and a stopping rule, so the number of perturbation iterations does not have to be fixed ex ante.
The current manuscript studies the operating characteristics of the method in a Monte Carlo design and an empirical illustration. The aim is not to replace post-double selection, but to make aggregation across imputed and bootstrapped datasets more stable, interpretable, and computationally disciplined.
Current manuscript: non-peer-reviewed working paper.