TwinPoSI: Statistical Twins for Powerful Post-Selection Inference on Population-Based Regression Coefficients

Abstract

Post-selection inference (PoSI) quantifies uncertainty about regression coefficients after data-driven feature selection. A central question is the inferential target. Projection-based targets are the coefficients of the best linear approximation restricted to the selected features and depend on the selection procedure, whereas population-based targets are the selected features' coefficients in the full linear model and are often more relevant for scientific interpretation. The two targets can differ, even in sign. Existing PoSI methods largely focus on projection-based targets and may yield overly wide confidence intervals. We propose TwinPoSI (statistical twin post-selection inference), a method for powerful PoSI on population-based targets with false coverage rate (FCR) control. TwinPoSI leverages \textit{statistical twins}, defined as synthetic datasets generated from a fitted model to mimic the original data. With generating parameters known, statistical twins enable direct calibration of confidence intervals for bias introduced by data-dependent feature selection. We establish that TwinPoSI controls the FCR at the nominal level, up to Monte Carlo error and an asymptotically negligible approximation error. Moreover, in a Gaussian linear model with an orthogonal design, TwinPoSI uniquely attains the oracle average interval length to first order among the methods considered. Simulations show that TwinPoSI maintains reliable FCR control for both population-based and projection-based targets while yielding shorter confidence intervals and higher power than the competing methods. In riboflavin production data, TwinPoSI identifies associated genes, quantifies their directions and magnitudes of association, and yields the shortest average intervals among the methods considered.