Manual Page for Command >>>> DEVIATION


Syntax
>>>> DEVIATION: sigma (ADD NOISE)

Parent Command
all third-level commands in block > OBSERVATION

Subcommand
-

Description
This command specifies the standard deviation sigma of the observations. The squares of the standard deviations constitute the diagonal elements of the a priori covariance matrix C . zz The specified value sigma is assigned to all data points of the corresponding data set. It must be given in the same units as the data (see command >>>> FACTOR). Individual values for each calibration point can be explicitly specified using command >>>> COLUMN or >> COVARIANCE, or are calculated as a fraction of the measured value if using command >>>> RELATIVE. The standard deviation should represent the expected variability of the final residuals. In the absence of modeling errors, the standard deviation is equivalent to the measurement error. A reasonable value can be derived by visual examination of the data, i.e., by estimating the standard deviation of the differences between the observed values and a line representing the expected match; note that this procedure is based on the assumption that time averages can be used to calculate the ensemble average, i.e., that the data set is a result of an ergodic process. The inverse of the a priori covariance matrix is used to weight the fitting error. It also scales observations of different types and units. In the framework of maximum likelihood theory, the covariance matrix constitutes the stochastic model along with the assumption of normality and independence. The parameter estimates are not affected by the absolute values of sigma, but only by the ratios sigma /sigma . It is suggested, however, to use i j reasonable values that are related to the measurement error. If the final residuals are - on average - significantly larger than the a priori specified standard deviations, the Fisher model test fails. The a posteriori standard deviations of the final residuals are printed in the output for each data set for comparison purposes. If keyword ADD NOISE is present, Gaussian noise with zero mean and the given standard deviation is added to the data points. This option may be useful if error-free data were synthetically generated.

Alternative commands are:

>>>> DEVIATION: sigma
>>>> VARIANCE: sigma^2
>>>> WEIGHT: 1/sigma

The following command lines are thus equivalent:

>>>> standard DEVIATION: 0.1
>>>> VARIANCE: 0.01
>>>> WEIGHT: 10.0

Example
> OBSERVATION
>> PRESSURE
>>> ELEMENT : AA412
>>>> conversion FACTOR: 1E5 from [bar] to [Pa]
>>>> DATA on FILE: pressure.dat
>>>> standard DEVIATION: 0.05 [bar]
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See Also
>> COVARIANCE | >>>> AUTO | >>>> COLUMN | >>>> DEVIATION (p) | >>>> RELATIVE | >>>> VARIANCE | >>>> WEIGHT


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Page updated: July 29, 1997