The difficult and ubiquitous problems of multiplicities

Multiplicities are ubiquitous. They threaten every inference in every aspect of life. Despite the focus in statistics on multiplicities, statisticians underestimate their importance. One reason is that the focus is on methodology for known multiplicities. Silent multiplicities are much more important and they are insidious. Both frequentists and Bayesians have important contributions to make regarding problems of multiplicities. But neither group has an inside track. Frequentists and Bayesians working together is a promising way of making inroads into this knotty set of problems. Two experiments with identical results may well lead to very different statistical conclusions. So we will never be able to use a software package with default settings to resolve all problems of multiplicities. Every problem has unique aspects. And all problems require understanding the substantive area of application.