Confidence and Discoveries with E-values

We discuss systematically two versions of confidence regions: those based on p-values and those based on e-values, a recent alternative to p-values. Both versions can be applied to multiple hypothesis testing, and in this paper we are interested in procedures that control the number of false dis-coveries under arbitrary dependence between the base p- or e-values. We in-troduce a procedure that is based on e-values and show that it is efficient both computationally and statistically using simulated and real-world data sets. Comparison with the corresponding standard procedure based on p-values is not straightforward, but there are indications that the new one performs significantly better in some situations.