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Multivariate Statistik

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Zusammenfassung

In Kap. 9 werden die wichtigsten Techniken der multivariaten Statistik vorgestellt: die Hauptkomponentenanalyse und die Clusteranalyse in den Abschn. 9.2 und 9.5 sowie die Unabhängigkeitsanalyse, die eine nichtlineare Erweiterung der Hauptkomponentenanalyse ist, in Abschn. 9.3. Abschn. 9.4 führt in die Diskriminanzanalyse ein, die eine beliebte Methode zur Klassifizierung in den Geowissenschaften ist. Abschn. 9.6 führt in die multiple lineare Regression ein. Abschn. 9.7 demonstriert die Verwendung der Log-Ratio-Transformation von John Aitchison, um das Problem der geschlossenen Summe zu überwinden, das in multivariaten Datensätzen sehr häufig auftritt.

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Empfohlene Lektüre

  • Aitchison J (1984) The Statistical Analysis of Geochemical Composition. Math Geol 16(6):531–564

    Article  Google Scholar 

  • Aitchison J (1986) Reprinted 2003 The Statistical Analysis of Compositional Data. The Blackburn Press, Caldwell

    Book  Google Scholar 

  • Aitchison J (1999) Logratios and Natural Laws in Compositional Data Analysis. Math Geol 31(5):563–580

    Article  Google Scholar 

  • Birks HJB, Gordon AD (1985) Numerical Methods in Quaternary Pollen Analysis. Academic, London

    Google Scholar 

  • Brown CE (1998) Applied Multivariate Statistics in Geohydrology and Related Sciences. Springer, Berlin

    Book  Google Scholar 

  • Davis JC (2002) Statistics and Data Analysis in Geology, 3. Aufl. Wiley, New York

    Google Scholar 

  • Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugen 7:179–188

    Article  Google Scholar 

  • Härdle WK, Simar L (2012) Applied Multivariate Statistical Analysis. Springer, Berlin

    Book  Google Scholar 

  • Hermanns R, Trauth MH, McWilliams M, Strecker M (2000) Tephrochronologic Constraints on Temporal Distribution of Large Landslides in NW-Argentina. J Geol 108:35–52

    Article  Google Scholar 

  • Hotelling H (1931) Analysis of a Complex of Statistical Variables with Principal Components. J Educ Psychol 24(6):417–441

    Article  Google Scholar 

  • Hyvärinen A (1999) Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks 10(3):626–634

    Article  Google Scholar 

  • MathWorks (2021a) Fuzzy Logic Toolbox – User’s Guide. The MathWorks Inc, Natick, MA

    Google Scholar 

  • MathWorks (2021b) Statistics and Machine Learning Toolbox – User’s Guide. The MathWorks Inc, Natick, MA

    Google Scholar 

  • Olorunfemi MO (1985) Statistical Relationships Among Some Formation Parameters for Sherwood Sandstone, England. Math Geol 17:845–852

    Article  Google Scholar 

  • Pawlowsky-Glahn V (2004) Geostatistical Analysis of Compositional Data – Studies in Mathematical Geology. Oxford University Press, Oxford

    Book  Google Scholar 

  • Pearson K (1901) On lines and planes of closest fit to a system of points in space. Philos. Mag J Sci 6(2):559–572

    Article  Google Scholar 

  • Reyment RA, Savazzi E (1999) Aspects of Multivariate Statistical Analysis in Geology. Elsevier Science, Amsterdam

    Google Scholar 

  • Streckeisen A (1976) To each plutonic rock its proper name. Earth-Science Reviews 12:1–33

    Article  Google Scholar 

  • Swan ARH, Sandilands M (1995) Introduction to Geological Data Analysis. Blackwell Sciences, Oxford

    Google Scholar 

  • Trauth MH, Bookhagen B, Mueller A, Strecker MR (2003) Erosion and climate change in the Santa Maria Basin, NW Argentina during the last 40,000 yrs. J Sediment Res 73(1):82–90

    Article  Google Scholar 

  • Weltje GJ, Tjallingii R (2008) Calibration of XRF core scanners for quantitative geochemical logging of sediment cores: Theory and application. Earth and Planetary Science Letters 274:423–438

    Article  Google Scholar 

  • Westgate JA, Shane PAR, Pearce NJG, Perkins WT, Korisettar R, Chesner CA, Williams MAJ, Acharyya SK (1998) All Toba Tephra Occurrences Across Peninsular India Belong to the 75,000 yr BP Erup-tion. Quaternary Research 50:107–112

    Article  Google Scholar 

  • Zadeh L (1965) Fuzzy sets. Information Control 8:338–353

    Article  Google Scholar 

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Authors and Affiliations

  1. Institut für Geowissenschaften, Universität Potsdam, Potsdam, Deutschland

    Martin H. Trauth

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  1. Martin H. Trauth
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Correspondence to Martin H. Trauth .

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© 2022 Der/die Autor(en), exklusiv lizenziert durch Springer-Verlag GmbH, DE, ein Teil von Springer Nature

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Trauth, M.H. (2022). Multivariate Statistik. In: MATLAB®-Rezepte für die Geowissenschaften. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-64357-0_9

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