  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 maximum likelihood estimation
in Panigrahi and Taylor (2022). Yet our pivot always produces narrower
confidence intervals than a closely related data splitting procedure. We
investigate the trade-off between power and exact selective inference on
simulated datasets and an HIV drug resistance dataset.
