RECAP: Representation-Based Calibration with Amortized Pooling for Frequentist Simulation-Based Inference

Abstract

Simulation-based inference enables uncertainty quantification in broad contexts when a simulation model is available but when a test statistic's sampling distribution is not tractable. But, frequentist calibration in this setting can be costly over high-dimensional parameter spaces. In this paper, we introduce RECAP (REpresentation-based Calibration with Amortized Pooling), a general framework for frequentist simulation-based inference. RECAP exploits low-dimensional structure in how the null distribution varies with parameters and is particularly useful when the parameter dimension is high or when different parameter configurations have redundant or compensating effects. RECAP pools simulated scores according to a representation that preserves this distribution exactly or approximately, allowing distant parameter values to share calibration information. Representations may be derived from model structure or learned independently. Empirical quantiles of the pooled scores then yield tests and confidence sets, for which we establish theoretical coverage guarantees. In the simulation studies, we show that RECAP has lower coverage error than existing approaches and power close to that of the point-wise oracle, while maintaining the computational benefits of amortized calibration. An application to population genomics illustrates learned low-dimensional calibration and interpretable uncertainty quantification.