View source for Evaluation modes

[[Category:Evaluation]] 
[[Category:Distribution_Functions|Distribution Function]]
[[Category:Doc_Status_D]] <!-- For Lumina use, do not change -->
 
There are two modes, "Mid" and "Prob", used to evaluate a variable or other expression. They each compute a different type of value:  
* The '''Mid value''' is  deterministic. It ignores any uncertainties. By default, when you ask for a Result -- a Table or Graph -- it first computes and shows the Mid value. This is much faster for a large model, since it only computes a single value for each distribution rather than a sample of numbers.  It uses the [[median]] of any probability distribution in a Definition, and the "Mid value" of any variable or function on which it depends.   The [[Mid]] value is often close to the [[Median]], but it is not guaranteed, to be equal because <code>Median(F(x, y))</code> is not always the same as <code>F(Median(x), Median(y))</code>. 

* The '''Prob value''' (probabilistic value) is a random sample of values from the probability distribution. It is also known as '''Sample evaluation mode'''. It evaluates any probability distribution in a definition -- e.g. <code>Normal(10, 5)</code> -- as a random sample using [[Monte Carlo]] or another [[sampling method]]. Each sample is an array indexed by the system index [[Run]] -- numbered from 1 to [[SampleSize]]. A Prob value for a variable or function uses the Prob value of any uncertain Variable or Function on which it depends.   When you select an [[Uncertainty view]] (other than "Mid") from the pulldown menu of a [[Result window]], it computes its "Prob value" and displays it as a Mean, Statistics, Probability Bands, PDF, or whichever option you select.  

If the variable has no "Prob value" because neither the variable nor any of its inputs contain a probability distribution, it gives a warning, and shows the Mid result. You can also select "Mid"  from the [[Uncertainty view of a result|Uncertainty view]]  to go back to see the [[Mid]] value (computing it if necessary).  

The accuracy with which the "Prob value" represents the underlying probability distribution increases with [[SampleSize]]. It usually makes sense to start with a small number -- e.g. the default 1000. You can increase it later when you have verified the model is correct, in the [[Uncertainty Setup dialog]] (available from the [[Result menu]]). 

[[Statistical functions]] -- such as [[Mean]], [[Sdeviation]], [[Correlation]] -- expect their main parameter(s) to be uncertain and evaluate them, and their predecessors, in Prob mode, even if they appear in an expression being evaluated in Mid mode. A statistical function estimates its value from a Prob value (or two Prob values, in the case of [[Correlation]], and related functions). If you define 

:<code>X := Mean(Y)</code>
:<code>Y := Normal(2, 1)</code>

If you evaluate «x» in Mid mode, the statistical function [[Mean]](y) will evaluate «y» in Prob mode. So, the Mid value of «x» will be an estimate of the mean of «y», based on a Monte Carlo sample which is the Prob value of <code>Y</code>. So, evaluating any variable containing a statistical function will cause a Prob mode evaluation of any variable appearing in its parameter(s), and any predecessors of those variables. The result of a statistical function is a Mid value, not a probability distribution. In the example above, <code>X</code> has a Mid value, equal to the mean of <code>Y</code>, but no Prob value. 

Conversely, the function [[Mid]](X) always evaluates its parameter «X» in Mid mode, even when [[Mid]](X) is evaluated in Prob mode. For example 

:<code>X := Mid(Y)</code>
:<code>Y := Uniform(10, 20)</code>

In this case, evaluating <code>X</code>, causes <code>Y</code> to be evaluated in Mid mode, returning the median of <code>y</code> (15). 

A is a function that returns a median value when evaluated in Mid-mode, and a sample array indexed by the [[Run]] Index when evaluated in [[Sample]]-mode. 

==See Also==
* [[Uncertainty views]]
* [[Mid]]()
* [[Sample]]
* [[IsSampleEvalMode]]
* [[Certain]]
* [[Statistical Functions and Importance Weighting]]
* [[Evaluate]]
* [[Objects and Values]]