Bayes/frequentist correspondences between the p-value and the posterior probability of the null hypothesis have been studied in univariate hypothesis testing situations. This paper extends these comparisons to multiple testing and in particular to the Bonferroni multiple testing method, in which p-values are adjusted by multiplying by k, the number of tests considered. In the Bayesian setting, ...

In this paper, we establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type ∑ π∈P(U)(−1)(|π| − 1)!f(π) where U is a finite set, P(U) is the partition lattice of U and f : P(U) → R is some suitable non-negative function. Applications of this new analogue are given to counting connected k-uniform hypergraphs, network reliability, and cum...

We present a unified approach to an important subclass of Bonferroni-type inequalities by considering so-called binomially bounded functions. Our main result associates with each binomially bounded function a Bonferroni-type inequality. By appropriately choosing this function, several well-known and new results are deduced.

In complex clinical trials, multiple research objectives are often grouped into sets of objectives based on their inherent hierarchical relationships. Consequently, the hypotheses formulated to address these objectives are grouped into ordered families of hypotheses and thus to be tested in a pre-defined sequence. In this paper, we introduce a novel Bonferroni based multiple testing procedure f...