Statistical information encoding

Statistical measures of variation of certain parameters and functions can be embedded in a DAVE-ML model. This information is captured in a uncertainty element, which can be referenced by variableDef, griddedTableDef and ungriddedTableDef elements.

Uncertainty in the value of a parameter or function is given in one of two ways, depending on the appropriate probability distribution function (PDF): as a Gaussian or normal distribution (bell curve) or as a uniform (evenly spread) distribution. One of these distributions is selected by including either a normalPDF or a uniformPDF element within the uncertainty element.

Linear correlation between the randomness of two or more variables or functions can be specified. Although the correlation between parameters do not have a dependency direction (that is, the statistical uncertainty of either parameter is specified in terms of the other one so the calculation order doesn't matter) correlation is customarily specified as a dependency of one random variable on the value of another random variable. correlatesWith identifies variables or functions whose uncertainty 'depends' on the current value of this variable or parameter; the correlation subelement specifies the correlation coefficient and identifies the (previously calculated) random variable or function on which the correlation depends.

These correlation subelements only apply to normal (Gaussian) probability distribution functions.

Each of these distribution description elements contain additional information, as described below.

    uncertainty : effect=['additive'|'multiplicative'|'percentage'|'absolute']
        normalPDF : numSigmas=['1', '2', '3', ...]
            bounds :
	   [correlatesWith : varID]
           [correlation : varID, corrCoef]
        uniformPDF : symmetric=['yes'|'no']
            bounds [, bounds]

uncertainty attributes:


Indicates, by choice of four enumerated values, how the uncertainty is modeled: as an additive, multiplicative, or percentage variation about the nominal value, or an specific number (absolute).

uncertainty sub-elements:


If present, the uncertainty in the parameter value has a probability distribution that is Gaussian (bell-shaped). A single parameter representing the additive (+/- some value), percentage (+/- some %) of variation from the nominal value in terms of 1, 2, 3, or more standard deviations (sigmas) is specified. Note here multiplicative and absolute bounds don't make much sense.


If present, the uncertainty in the parameter or function value has a uniform likelihood of taking on any value between symmetric or asymmetric boundaries, which are specified in terms of additive (either +/-x or +x/-y), multiplicative, percentage, or absolute variations. The specified range of values must bracket the nominal value. For this element, the bounds sub-element may contain one or two values in which case the boundaries are symmetric or asymmetric.