Approximate Selective Inference via Maximum Likelihood

Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy compute, while others fare better in terms inferential power. In this article, we consider a selective framework for Gaussian data. We propose new method through approximate maximum likelihood estimation. Our goal is to: (a) achieve power with the aid randomization, (b) bypass expensive MCMC sampling from exact conditional distributions that hard evaluate closed forms. construct inference, example, p-values, confidence intervals etc., by solving fairly simple, convex optimization problem. illustrate potential our across wide-ranging values signal-to-noise ratio simulations. On cancer gene expression dataset find improves upon commonly used inference. Supplementary materials article available online.