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By V.V. Fedorov

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Com). 3 Overview of applications to biomedical and genomic research The novel multiple testing procedures introduced above have been applied to a number of testing problems in biomedical and genomic research. Many of these applications concern microarray experiments, which are popular highthroughput assays for measuring the abundance of deoxyribonucleic acids (DNA) and ribonucleic acids (RNA) in different types of cell samples for thousands of sequences simultaneously (Phimister and Cohen, 1999; Packer, 2002; Packer and Axton, 2005; Speed, 2003).

Tau. edu/~genovese), and John Storey (faculty. edu/~jstorey). , 2001). Although such methods constitute an important alternative to frequentist approaches, their thorough treatment is beyond the scope of this book. 2 and discusses its software implementation and application to a variety of testing problems in biomedical and genomic research. The present chapter introduces a general statistical framework for multiple hypothesis testing and motivates the methods developed in Chapters 2–7. These methodological chapters provide specific multiple testing procedures for controlling a range of Type I error rates that are broadly defined as parameters Θ(FVn ,Rn ) of the joint distribution FVn ,Rn of the numbers of Type I errors Vn and rejected hypotheses Rn .

One could also consider the M = J(J −1)/2 submodels M(j, j ) = {P ∈ M : X(j) ⊥ X(j )}, j, j = 1, . . , J, j < j , corresponding to pairwise independence of the elements of X. , functions Ψ (P ) = ψ = (ψ(m) : m = 1, . . , M ) ∈ IRM of the data generating distribution P , and each null hypothesis H0 (m) refers to a single parameter, ψ(m) = Ψ (P )(m) ∈ IR. One distinguishes between two types of testing problems for such parametric hypotheses, one-sided and two-sided tests. 2 Multiple hypothesis testing framework One-sided tests H0 (m) = I (ψ(m) ≤ ψ0 (m)) vs.

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