We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce the problem of exact selective inference to a bivariate truncated Gaussian distribution. By doing so, we give up some power that is achieved with approximate inference in Panigrahi and Taylor (2022). Yet we always produce narrower confidence intervals than a closely related data-splitting procedure. For popular instances of Gaussian regression, this price -- in terms of power -- in exchange for exact selective inference is demonstrated in simulated experiments and in an HIV drug resistance analysis.

翻译：我们引入了一种用于基于随机化的精确选择性推断的枢轴量。该枢轴量不仅能在高斯回归模型中实现精确推断，而且具有闭合形式的解析解。我们将精确选择性推断问题简化为一个二元截断高斯分布问题。虽然这种方法相比Panigrahi和Taylor（2022）中近似推断方法牺牲了一定统计功效，但总能产生比密切相关的数据分割方法更窄的置信区间。针对高斯回归的典型应用场景，我们通过模拟实验和HIV耐药性分析，展示了这种以统计功效换取精确选择性推断的代价。