### 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.

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

```    uncertainty : effect=['additive'|'multiplicative'|'percentage'|'absolute']
EITHER
normalPDF : numSigmas=['1', '2', '3', ...]
bounds :
OR
uniformPDF : symmetric=['yes'|'no']
bounds [, bounds]
```

uncertainty attributes:

effect

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:

normalPDF

If present, the uncertainty in the parameter value has a probility 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 multplicative and absolute bounds don't make much sense.

uniformPDF

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.

TBD