Abstract: We develop measures of uncertainty, including model confidence sets and a LogP measure, for shrinkage model selection procedures. The measures are developed for linear models, generalized linear models, and generalized additive models. We study the theoretical and empirical properties of the proposed measures, and demonstrate how theses measures work by applying them to real-life problems.

Key words and phrases: Asymptotic coverage probability, average probability of coverage, consistency, nested MCS, shrinkage model selection, uncertainty.