## Abstract

When drawing large-scale simultaneous inference, such as in genomics and imaging problems, multiplicity adjustments should be made, since, otherwise, one would be faced with an inflated type I error. Numerous methods are available to estimate the proportion of true null hypotheses π_{0}, among a large number of hypotheses tested. Many methods implicitly assume that the π_{0} is large, that is, close to 1. However, in practice, mid-range π_{0} values are frequently encountered and many of the widely used methods tend to produce highly variable or biased estimates of π_{0}. As a remedy in such situations, we propose a hierarchical Bayesian model that produces an estimator of π_{0} that exhibits considerably less bias and is more stable. Simulation studies seem indicative of good method performance even when low-to-moderate correlation exists among test statistics. Method performance is assessed in simulated settings and its practical usefulness is illustrated in an application to a type II diabetes study.

Original language | English (US) |
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Pages (from-to) | 222-232 |

Number of pages | 11 |

Journal | Biometrical Journal |

Volume | 52 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2010 |

## Keywords

- Bayesian framework
- Microarray data
- Mixture model
- Multiple testing
- Robustness

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty