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Posterior consistency of Dirichlet mixtures of beta densities in estimating positive false discovery rates | | Subhashis Ghosal
; Anindya Roy
; Yongqiang Tang
; | | Date: |
15 May 2008 | | Abstract: | In recent years, multiple hypothesis testing has come to the forefront of
statistical research, ostensibly in relation to applications in genomics and
some other emerging fields. The false discovery rate (FDR) and its variants
provide very important notions of errors in this context comparable to the role
of error probabilities in classical testing problems. Accurate estimation of
positive FDR (pFDR), a variant of the FDR, is essential in assessing and
controlling this measure. In a recent paper, the authors proposed a model-based
nonparametric Bayesian method of estimation of the pFDR function. In
particular, the density of p-values was modeled as a mixture of decreasing beta
densities and an appropriate Dirichlet process was considered as a prior on the
mixing measure. The resulting procedure was shown to work well in simulations.
In this paper, we provide some theoretical results in support of the beta
mixture model for the density of p-values, and show that, under appropriate
conditions, the resulting posterior is consistent as the number of hypotheses
grows to infinity. | | Source: | arXiv, 0805.2264 | | Services: | Forum | Review | PDF | Favorites | |
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