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## Error Models

SimBiology® supports the error models described in the following table. For instance, if you assume every observation has a constant amount of noise, use the constant error model, which is the default. Instead, if you assume the error is proportional to the response data, then the proportional error model might be more appropriate.

Error ModelMathematical RepresentationStandard Deviation of Error Model
constant (default)$y=f+a\epsilon$a
proportional$y=f+b|f|\epsilon$ b|f|
combined$y=f+\left(a+b|f|\right)\epsilon$a+b|f|
exponential$y=f\ast \mathrm{exp}\left(a\epsilon \right)$ or equivalently,$\sqrt{{e}^{{a}^{2}}-1}*{e}^{a}$
$\mathrm{log}\left(y\right)=\mathrm{log}\left(f\right)+a\epsilon$a
Here, y is the response, f is the function value, ɛ is a standard mean-zero and unit-variance (Gaussian) variable, and a and b are error parameters. For instance, if you assume the error is approximately 5% of each observation, use the proportional error model with b = 0.05. In SimBiology, f typically represents the simulation result.

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