A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing

By Malgorzata Bogdan, Jayanta Kumar Ghosh, Surya T. Tokdar. 2008

108 citations recorded by the source corpus.

In the spirit of modeling inference for microarrays as multiple testing for sparse mixtures, we present a similar approach to a simplified version of quantitative trait loci (QTL) mapping. Unlike in case of microarrays, where the number of tests usually reaches tens of thousands, the number of tests performed in scans for QTL usually does not exceed several hundreds. However, in typical cases, the sparsity $p$ of significant alternatives for QTL mapping is in the same range as for microarrays. For methodological interest, as well as some related applications, we also consider non-sparse mixtures. Using simulations as well as theoretical observations we study false discovery rate (FDR), power and misclassification probability for the Benjamini-Hochberg (BH) procedure and its modifications, as well as for various parametric and nonparametric Bayes and Parametric Empirical Bayes procedures. Our results confirm the observation of Genovese and Wasserman (2002) that for small p the misclassification error of BH is close to optimal in the sense of attaining the Bayes oracle. This property is shared by some of the considered Bayes testing rules, which in general perform better than BH for large or moderate $p$'s.

Subfields: Management Science and Operations Research, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c174f3cd783f6d7c60f45465a11531dad3ec0ceb

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Citations in the corpus

Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction (2012, background): “Many of this framework's asymptotic properties are well understood, both as the number of means (p) and the number of replicated observations (n) grow [Johnstone and Silverman, 2004, Scott and Berger, 2006, 2010, Muller et al., 2006, Bogdan et al., 2008a,b].”
Toward enhanced understanding and projections of climate extremes using physics-guided data mining techniques (2014, methodology): “…false discoveries is still an active research area and several new methods have been proposed in last two decades (Benjamini and Hochberg, 1995; Bogdan et al., 2008; Dudoit et al., 2003; Efron, 2007) that improve upon the Bonferroni theorem both by new methodological and theoretical developments.”
The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors (2014, unknown): “Their references for this statement, Scott and Berger (2010) and Bogdan, Ghosh and Tokdar (2008), indicate that they are thinking of a marginal maximum likelihood estimate of τ .”
Asymptotic Properties of Bayes Risk of a General Class of Shrinkage Priors in Multiple Hypothesis Testing Under Sparsity (2013, methodology): “Note that the above estimator of τ is truncated below by 1m and hence it is not susceptible to collapsing to zero, which is a major concern for the use of such empirical Bayes approaches as mentioned in Carvalho et al. (2009), Scott and Berger (2010), Bogdan et al. (2008) and Datta and Ghosh (2013).”
Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem (2010, background): “1 Supported in part by the U.S. National Science Foundation under a Graduate Research Fellowship and Grants AST-0507481 and DMS-01-03265.”
CONSISTENCY OF A RECURSIVE ESTIMATE OF MIXING DISTRIBUTIONS (2009, background): “In microarray analysis [29] or quantitative trait loci (QTL) mapping [3], each θ represents the expression level of a single gene or the association level of a single genetic marker, respectively.”
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, methodology): “Extensive simulation studies and theoretical calculations in [6, 23] and [5] illustrate that multiple testing rules controlling the BFDR at a small level α ≈ 0.”