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To proceed further, we express the prediction error ε[k] in terms of the actual states and the estimated states.
The above described performance criteria do not express the prediction ability of the model precisely from higher to low flow region.
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Another way of expressing the prediction error is through the Relative Squared Error (RS E– Equation 6), Root Relative Squared Error (RRS E– Equation 7), and Relative Absolute Error (RAE – Equation 8).
Otherwise, a good way of expressing the prediction performance is through relative errors such as the Mean Relative Error (MRE – Equation 4) and Mean Relative Squared Error (MRS E– Equation 5).
We can then express the (α−1 th prediction errors as.
In the hydrodynamic and water quality modeling (Havens and James, [2005]; Havens et al., [2004]), it is often useful to express the observation-prediction discrepancies in percentage to measure the model performance.
From the confusion matrices that were obtained, the mean value of each element was computed to express the global model prediction.
where (hat {epsilon }(i)) expresses the estimated prediction error after adding a new center and (bar {epsilon }(i)) is the approximated prediction error after merging.
where (hat {epsilon }(i)) expresses the estimated prediction error after discarding an existing center, while (bar {epsilon }(i)) is the approximated prediction error of keeping this center.
To quantify which upstream positions had been most optimized in terms of predicted targeting enhancing elements in the three Arabidopsis proteins of interest, we expressed the PWM prediction score s of a mutated residue r at position sr,x relative to the difference between minimum and maximum score in percentage [(smax,x-sr,x / smax,x-smin,x) *100].
With some algebra manipulations, we may express the n-step ahead prediction probability (hat {b}(t + n)) as hat{b}(t + n) = frac{beta}{alpha+beta}-frac{beta}{alpha+beta} (1 - alpha - beta)^{n}+(1 - alpha - beta)^{n}b t).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com