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Statistical Methods in High Dimensions

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Phenotypes and Genotypes

Part of the book series: Computational Biology ((COBO,volume 18))

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Abstract

This is the core chapter that introduces the theory related to the advanced statistical methods applied in the later chapters on QTL mapping and GWAS analysis. More basic statistical methods are included in the Appendix. Section 3.2 covers the use of classical procedures, like the Bonferroni correction, in multiple testing, as well as approaches based on permutation and resampling, which guarantee control of the familywise error rate (FWER). Afterwards, more modern techniques, like the Benjamini-Hochberg procedure to control the false discovery rate (FDR), are discussed and a somewhat advanced theoretical discussion on optimal multiple testing strategies in high dimensions follows. The second part of this chapter is concerned with model selection. Section 3.3 starts by introducing the basic concepts of likelihood and then recapitulates the development of Akaike’s information criterion (AIC) using information theoretic principles. This is then compared with the use of the Bayesian information criterion (BIC) in the context of Bayesian model selection. It is then pointed out why both AIC and BIC fail to work in a high-dimensional setting and different modifications of BIC designed to control either FWER or FDR are presented. The chapter ends by discussing various further approaches to model selection in high dimensions.

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Authors and Affiliations

  1. Center for Medical Statistics, Informatics, and Intelligent Systems Section for Medical Statistics, Medical University of Vienna, Spitalgasse 23, 1090, Vienna, Austria

    Florian Frommlet

  2. Institute of Mathematics, University of Wrocław, Wrocław, Poland

    Małgorzata Bogdan

  3. Department of Operations Research, Wrocław University of Technology, Wrocław, Poland

    David Ramsey

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  1. Florian Frommlet
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  2. Małgorzata Bogdan
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  3. David Ramsey
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Correspondence to Florian Frommlet .

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Frommlet, F., Bogdan, M., Ramsey, D. (2016). Statistical Methods in High Dimensions. In: Phenotypes and Genotypes. Computational Biology, vol 18. Springer, London. https://doi.org/10.1007/978-1-4471-5310-8_3

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  • DOI: https://doi.org/10.1007/978-1-4471-5310-8_3

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