Inference after model selection presents computational challenges when dealing with intractable conditional distributions. Markov chain Monte Carlo (MCMC) is a common method for sampling from these distributions, but its slow convergence often limits its practicality. In this work, we introduce a method tailored for selective inference in cases where the selection event can be characterized by a polyhedron. The method transforms the variables constrained by a polyhedron into variables within a unit cube, allowing for efficient sampling using conventional numerical integration techniques. Compared to MCMC, the proposed sampling method is highly accurate and equipped with an error estimate. Additionally, we introduce an approach to use a single batch of samples for hypothesis testing and confidence interval construction across multiple parameters, reducing the need for repetitive sampling. Furthermore, our method facilitates fast and precise computation of the maximum likelihood estimator based on the selection-adjusted likelihood, enhancing the reliability of MLE-based inference. Numerical results demonstrate the superior performance of the proposed method compared to alternative approaches for selective inference.

翻译：模型选择后的推断在面临难以处理的條件分布时带来了计算挑战。马尔可夫链蒙特卡洛（MCMC）是从这些分布中采样的常用方法，但其收敛速度缓慢往往限制了其实用性。本文针对选择事件可由多面体描述的情形，提出了一种专用于选择性推断的方法。该方法将受多面体约束的变量转换为单位立方体内的变量，从而能够利用常规数值积分技术进行高效采样。与MCMC相比，所提采样方法具有高精度，并附带误差估计。此外，我们引入了一种方法，可利用单批样本对多个参数进行假设检验和置信区间构建，从而减少重复采样的需求。进一步，我们的方法能够基于选择调整似然快速精确地计算最大似然估计，增强了基于MLE的推断的可靠性。数值结果表明，与选择性推断的替代方法相比，所提方法具有更优越的性能。