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Fix description of scaling
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sahle authored May 22, 2024
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<div class="col-xs-12">
<p>
Before you can execute a parameter estimation task you need to specify the dataset which COPASI will use to fit the
parameters you have specified. Each experiment of your dataset contributes to the objective function with the
parameters you have specified.
The data can provided in any number of data files that can each contain one or more experiments, each experiment
containing one or several data columns.
All data points in the columns of all experiments contribute to the objective function with the
following weighted sum of squares:</p>
<p>
$$E(P)=\sum_{i,j}\omega_{j}\cdot(x_{i,j}-y_{i,j}(P))^{2}$$
</p>
<p>
Where $P$ is the currently tested parameter set, $x_{i,j}$ is a point in the dataset, and $y_{i,j}(P)$ the corresponding
simulated value. The indices $i$ and $j$ denote rows and columns in the dataset. The weight for each data column is given
by $\omega_{j}$. COPASI provides 4 methods shown in the table below
to calculate the weights for you. After applying the method chosen COPASI scales the weights so that for each
experiment the maximal occurring weight is $1$. In case that the weights calculated are not satisfactory you are able
to manually override them individually. To overwrite that behavior you can choose to check the
<b>Normalize Weights per Experiment</b> option. </p>
simulated value. The indices $i$ and $j$ denote rows and columns in the dataset. The weight $\omega_{j}$ is specified
for each data column and can either be provided by the user or calculated automatically by COPASI. In the user interface,
weights that are calculated by COPASI are displayed in brackets.
The weights are intended to adjust the contributions of the different data columns to the overall objective function so
that ideally data points from each column contribute equally.
For the calculation of the weights COPASI offers three different methods that are based on different assumptions about how
residual error scales with the data values.
Depending on whether the <b>Normalize Weights per Experiment</b> Checkbox is ticked, the weights are scaled so that the largest
weight for any data column in the complete set is $1$, or that the largest weight in each single experiment is $1$.

To manually adjust the weight values you can simple override them by entering new values in the table. </p>


<table class="table table-striped" style="caption-side: top;">
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bottom of the dialog by selecting the method from the drop down list. For an explanation of the individual methods,
please consult the methods section.</p>
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