Given:

• a function  $//<![CDATA[ \begin{array}{l}y^*(x, {\bf p})\end{array} //]]>$ of the argument  $//<![CDATA[ \begin{array}{l}x\end{array} //]]>$ and set of model parameters  $//<![CDATA[ \begin{array}{l}{\bf p} = \{ p_m\}_{m = 1..M} = \{p_1, p_2, ... p_M\}\end{array} //]]>$
• a discrete finite training dataset:  $//<![CDATA[ \begin{array}{l}\{ (x_k, y_k)\}_{k = 1..N} = \{ (x_0, y_0), (x_1, y_1), ..., (x_N, y_N) \}\end{array} //]]>$ representing the available knowledge about the system the model is trying to describe

then matching procedure assumes searching for the specific set of model parameters  $//<![CDATA[ \begin{array}{l}{\bf p}_{\rm bestfit}\end{array} //]]>$ to minimize the goal function:

where  $//<![CDATA[ \begin{array}{l}\Psi(z)\end{array} //]]>$ is the discrepancy distance function.

The most popular choices are $//<![CDATA[ \begin{array}{l}\Psi(z) = z^2\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}\Psi(z) = |z|\end{array} //]]>$.

See also

Human / Science / Formal Science / System Science / System Model