Abstract
In this work we investigate the properties of the statistical power of the Benjamini-Hochberg procedure. That procedure provides a widely used method for controlling the False Discovery Rate in a multiple comparison setup. We show that in many cases the statistical power of the p-values adjusted by the Benjamini-Hochberg procedure could be approximated by a normal distribution with both its mean and standard deviation having an exponential fit and convergence when the number of tests increase. As a result one could estimate the probability that the power belongs in a predetermined interval in a very computationally efficient way using only simulations for several values of the number of tests parameter. The fit for the mean also supports the conjecture that the power of the test decreases to the limit power, which is known to exist, when increasing the number of tests. The latter is a very favourable observation from practical perspective and we try to offer partially rigorous explanation why the monotonicity is present.
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References
Atanassov, E., Gurov, T., Ivanovska, S., Karaivanova, A.: Parallel monte carlo on intel MIC architecture. Procedia Comput. Sci. 108, 1803–1810 (2017)
Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. R. Stat. Soc. Ser. B (Methodol.) 57(1), 289–300 (1995)
Benjamini, Y., Yekutieli, D.: The control of the false discovery rate in multiple testing under dependency. The Annals of Statistics 29(4), 1165–1188 (2001)
Ferreira, J.A., Zwinderman, A.H.: On the Benjamini - Hochberg method. Ann. Statist. 34(4), 1827–1849 (2006)
Li, J., Witten, D.M., Johnstone, I.M., Tibshirani, R.: Normalization, testing, and false discovery rate estimation for RNA-sequencing data. Biostatistics 13(3), 523–538 (2012)
Storey, J.D., Taylor, J.E., Siegmund, D.: Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: A unified approach. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 66(1), 187–205 (2004)
Van Noorden, R., Maher, B., Nuzzo, R.: The top 100 papers. Nature 514(7524), 550–553 (2014)
Acknowledgements
This work has been supported by grant DN-02/13 (Modern mathematical methods for Big data) with Bulgarian NSF.
The extensive numerical calculations were performed on the HPC facility Avitohol of IICT-BAS, described in [1].
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Palejev, D., Savov, M. (2021). Estimating the Statistical Power of the Benjamini-Hochberg Procedure. In: Dimov, I., Fidanova, S. (eds) Advances in High Performance Computing. HPC 2019. Studies in Computational Intelligence, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-55347-0_26
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DOI: https://doi.org/10.1007/978-3-030-55347-0_26
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