Invariants and Homomorphisms Implicit in, and the Invalidity of the Mean-Variance Framework and Other Causality Approaches: Some Structural Effects

  • Michael I. C. Nwogugu


Many aspects of modern statistical analysis, Data Science and optimization are based almost entirely on the Mean–Variance (M-V) Framework and its elements—Variance, Semivariance, Correlation and Covariance. This chapter explains why these measures are very inaccurate and don’t reflect reality and also introduces Invariants for analysis of rates-of-change and Pattern Formation. That is, some of the illustrated limitations of the M-V Framework are Invariants that present new opportunities in computing and computational methods in various fields including Optimization, Pattern Formation, Chaos and Evolutionary Computation, given the discussions in Sandfeld and Zaiser (Modelling and Simulation in Materials Science and Engineering, 23(6), 065005, 2015), Kriener et al. (Frontiers of Computational Neuroscience, 7, 187–191, 2014), Fenn et al. (Physics Review E, 84, 61–65, 2011), Preis et al. (Scientific Reports, 2, Article number: 752, 2012), Kenett et al. (International Journal of Bifurcation & Chaos, 22, 1250181, 2012), Pearson (Philosophical Transactions of the Royal Society of London Series A, 186, 343–414, 1895), Fuwape and Ogunjo (CBN Journal of Applied Statistics, 4(2), 129–134, 2013), Menna et al. (International Journal of Modern Physics C, 13(1), 31–39, 2002), Egozcue (Cogent Mathematics, 2(1), 991082, 2015), and Andrade et al. (Physica D: Nonlinear Phenomena, 223(2), 139–145, 2006), all of which omitted the limitations. One of the biggest problems inherent in the M-V Framework is that its main components (Variance, Covariance, Correlation and Semivariance) measure the results but not the causes of variation and covariation.


Mean–Variance Framework Risk analysis Decision-making Portfolio management Optimization Pattern recognition Data science 


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Authors and Affiliations

  • Michael I. C. Nwogugu
    • 1
  1. 1.EnuguNigeria

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