  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 discoveries under
arbitrary dependence between the base p- or e-values. We introduce a procedure
that is based on e-values and show that it is efficient both computationally
and statistically using simulated and real-world datasets. 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.
