Symmetric mean squared error

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AmP estimation
Concepts

Data and completeness
Parameter estimation
Goodness-of-fit: SMSE / MRE
AmP Literature

Practice - essentials

Starting an estimation for a new species
Setting initial parameter values
Setting weight coefficients
Computing implied properties
Submitting to the collection

Practice - extra modules
Code specification
User-defined files: run, mydata, pars_init, predict
Data: Zero-variate, Univariate, Pseudo-data

Typified models
Estimation options

For each entry a Symmetric Mean Squared Error (SMSE) is computed to help judge the goodness of fit.

Definition

To compute the SMSE we start by computing the Symmetric Squared Error (SSE) for each data set. The SSE of a data set is computed in this way

SSE.png for SumWeights.png

where i refers to the data set and j to a given point in data set i. dij stands for the data, pij for the model prediction and wij for the associated weight coefficient. Finally, di and pi in the denominator represent, respectively, the average of all data points (dij) and predictions (pij) in set i:

Mean d.png and Mean p.png

In the case the sum of the weights wi is equal to zero we simply take the error to be zero. The implication is that this data set does not contribute to the SMSE.

SMSE is then the mean of all SSEi with wi greater than 0.

SMSE SSE.png

where n' is the number of data sets with wi greater than 0.

The zerovariate case

In the case of a zero-variate data set the relative error simplifies to

SSE0var.png

and the connection with the formal definition of relative is more easily seen.