In epidemiology, earthquakes, tokamak disruptions etc., there is possibility of approximations with the sequence of Gaussians and with the appropriate risks ( see my papers in Journal of Fusion Energy, 2015 and International Journal of Molecular and Theoretical Physics, 2017 ). What is the role of thresholding and bifurcations?
It doesn’t seem useful, since Gaussians have a scale-their width-while power law distributions don’t have a scale.
What is with the following case. Consider an ill-posed inverse problem where a physical quantity f needs to be recovered from an indirect measurement m modeled by m= Af+w where m is the measurement data vector, A is an operator (action) modeling the measurement and w is white noise. In Bayesian inversion, the quantities m,f and w are considered as random variables. Bayesian inversion generalizes deterministic regularization (Tihonov) and yields information abot the structure of ill posed inverse problem.
Dear Dr Danilo: A power law is often represented by an equation with an exponent: Y=MX^B. Each letter represents a number. Y is a function (the result); X is the variable (the thing you can change); B is the order of scaling (the exponent), and M is a constant (unchanging). For more on this and germane to your question , please have a look at :
https://www.sciencedirect.com/topics/engineering/power-law-model
Regards--
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