Mind the bias!

S.M. Papalexiou, D. Koutsoyiannis, and A. Montanari, Mind the bias!, STAHY Official Workshop: Advances in statistical hydrology, Taormina, Italy, doi:10.13140/RG.2.2.12018.50883, International Association of Hydrological Sciences, 2010.



Most statistical procedures, including parameter estimation and hypothesis testing, are based on a tacit assumption of a statistical sample consisted of independent random variables. This is not consistent with geophysical processes, which usually exhibit a strong temporal dependence, often of long range. Such dependence implies substantial negative bias in the estimation of statistical parameters of dispersion, e.g., variance, as well as parameters of dependence, e.g., autocorrelation. Failure to account for this bias leads to distorted picture of the underlying process and results in erroneous modelling and prediction. Here we demonstrate the impact of neglecting dependence in parameter estimators by using synthetic examples from stochastic processes with sort- and long-range dependence, as well as rainfall datasets that exhibit high temporal dependence. We also propose a methodology to correctly account for the bias.

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See also: http://dx.doi.org/10.13140/RG.2.2.12018.50883

Our works that reference this work:

1. D. Koutsoyiannis, A. Paschalis, and N. Theodoratos, Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields, Journal of Hydrology, 398 (1-2), 91–100, 2011.
2. D. Koutsoyiannis, P. Dimitriadis, F. Lombardo, and S. Stevens, From fractals to stochastics: Seeking theoretical consistency in analysis of geophysical data, Advances in Nonlinear Geosciences, edited by A.A. Tsonis, 237–278, doi:10.1007/978-3-319-58895-7_14, Springer, 2018.
3. Y. Markonis, Y. Moustakis, C. Nasika, P. Sychova, P. Dimitriadis, M. Hanel, P. Máca, and S.M. Papalexiou, Global estimation of long-term persistence in annual river runoff, Advances in Water Resources, 113, 1–12, doi:10.1016/j.advwatres.2018.01.003, 2018.