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For a system with N interacting particles in Z = X × Y the mutual information is approximated by (this is I(2) in (Kraskov et al.2004)): I cont ( X ; Y ) ≈ ψ ( N ) + ψ ( k ) − 1 / k − 〈 ψ ( n x ) + ψ ( n y ) 〉 (20).
They found that the set of periods that maximizes the Fisher information is approximated by a geometric series in a regime of large-scale ratios.
For the common case of incomplete data, the missing information is approximated to "typical" values or is randomly generated to create an ensemble of models that are screened for models that agree with experimental observations [ 20].
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To address this challenge, we propose a method where random variables comprising equivalence classes constrained by the available information are approximated using polynomial chaos expansions (PCEs).
To tackle the non-convex problem, the exact expression of the wireless information throughput is approximated by the high signal to noise ratio (SNR) approximation method, which is shown very tight to the exact expression.
(Data is approximate, tracking by Google Analytics).
The explanatory variable of interest is naturalisation, which is approximated by using information on place of birth and nationality.
The Hessian is approximated as a product of the Jacobian to obtain second derivative information [ 29].
The output size is approximated.
In prior work, this information has been approximated by using LD information from 'best guess' reference panels, but here we show that this can lead to high error rates even when a population closely matching the study population is available (Zaitlen et al.., 2009).
In some cases, local information can be approximated by L-numbers discovered by Lorden, and simple rules based on these approximations are asymptotically optimal to better order than the cost for a single observation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com