Constructing valid confidence sets is a crucial task in statistical inference, yet traditional methods often face challenges when dealing with complex models or limited observed sample sizes. These challenges are frequently encountered in modern applications, such as Likelihood-Free Inference (LFI). In these settings, confidence sets may fail to maintain a confidence level close to the nominal value. In this paper, we introduce two novel methods, TRUST and TRUST++, for calibrating confidence sets to achieve distribution-free conditional coverage. These methods rely entirely on simulated data from the statistical model to perform calibration. Leveraging insights from conformal prediction techniques adapted to the statistical inference context, our methods ensure both finite-sample local coverage and asymptotic conditional coverage as the number of simulations increases, even if n is small. They effectively handle nuisance parameters and provide computationally efficient uncertainty quantification for the estimated confidence sets. This allows users to assess whether additional simulations are necessary for robust inference. Through theoretical analysis and experiments on models with both tractable and intractable likelihoods, we demonstrate that our methods outperform existing approaches, particularly in small-sample regimes. This work bridges the gap between conformal prediction and statistical inference, offering practical tools for constructing valid confidence sets in complex models.

翻译：构建有效的置信集是统计推断中的关键任务，然而传统方法在处理复杂模型或有限观测样本量时常常面临挑战。这些挑战在现代应用中经常遇到，例如无似然推断。在这些场景中，置信集可能无法维持接近名义值的置信水平。本文介绍了两种新方法，TRUST 和 TRUST++，用于校准置信集以实现无分布条件覆盖。这些方法完全依赖于统计模型的模拟数据来执行校准。借鉴并适用于统计推断背景的共形预测技术，我们的方法确保了有限样本局部覆盖以及随着模拟次数增加而达到的渐近条件覆盖，即使样本量 n 很小。它们能有效处理冗余参数，并为估计的置信集提供计算高效的不确定性量化。这使得用户可以评估是否需要额外的模拟来进行稳健推断。通过对具有可处理及不可处理似然模型的理論分析和实验，我们证明了我们的方法优于现有方法，尤其是在小样本情况下。这项工作弥合了共形预测与统计推断之间的差距，为在复杂模型中构建有效置信集提供了实用工具。