Difference between revisions of "Evaluation modes"

Latest revision as of 01:22, 26 November 2024

All variables have a Mid' or deterministic value, computed in "Mid mode". Some also have a '"Prob"' or probabilistic value, computed in "Prob mode":

The Mid value is a deterministic value that ignores any uncertainties, shown when computed in "Mid mode". 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 Median(F(x, y)) is not always the same as F(Median(x), Median(y)). By default, when you first ask for a Result -- e.g. to view a Table or Graph -- it first computes and shows the Mid value. A Mid value is much faster to compute for a large model, since it uses only a single value for each distribution rather than a random sample of numbers.

The Prob (probabilistic) value is a random sample of values from a probability distribution. Prob values are computed in Sample evaluation mode. Any probability distribution in a definition -- e.g. Normal(10, 5) -- is evaluated 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 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

X := Mean(Y)

Y := Normal(2, 1)

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 Y. 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, X has a Mid value, equal to the mean of Y, 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

X := Mid(Y)

Y := Uniform(10, 20)

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

@@ Line 1: / Line 1: @@
-[[category:Concepts]]
+[[Category:Evaluation]]
-(in progress)
+[[Category:Distribution_Functions|Distribution Function]]
-Analytica's computational engine evaluates ''expressions''. When you view a result for a variable, Analytica evaluates the expression stored in that variable's definition attribute.
+[[Category:Doc_Status_D]] <!-- For Lumina use, do not change -->
+All variables have a  '''Mid'''' or deterministic value, computed in "Mid mode".  Some also have a '"Prob"' or probabilistic value, computed in "Prob mode":
+* The '''Mid''' value is a deterministic value that ignores any uncertainties, shown when computed in "Mid mode". 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>.  By default, when you first ask for a Result -- e.g. to view a Table or Graph -- it first computes and shows the Mid value. A Mid value is much faster to compute for a large model, since it uses only a single value for each distribution rather than a random sample of numbers.
-When you view a "Mid" result, Analytica evaluates the definition in '''''Mid-Mode'''''.  When you view any of the other result views (Mean, Stats, Bands, PDF or Prob Mass, CDF or Cum Prob, or Sample), Analytica evaluates the result in '''''Sample-mode'''''.  Sometimes the terms prob-mode or probability-mode are used synonymously to Sample-mode.  Some expression return different results in Mid-Mode and Sample-Mode.  These are usually expressions that have probabilistic results.
+* The '''Prob''' (probabilistic) value is a random sample of values from a probability distribution. Prob values are computed in '''Sample evaluation mode'''. Any probability distribution in a definition -- e.g. <code>Normal(10, 5)</code> -- is evaluated 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.
-A [[category:Distribution Functions|Distribution Function]] 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.
+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 evaluation mode (Mid or Sample) can change as sub-expressions are evaluated.  For example, the [[Mean]] function computes the mean of an uncertain quantity.  In order to do this, [[Mean]] requires the sample value.  So, when Mean(X+Y) is evaluated in ''Mid-Mode'', Analytica first evaluates X+Y in ''Sample-Mode'', then passes this value to the Mean function.
+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).
+==See Also==
+* [[Uncertainty views]]
+* [[Mid]]()
+* [[Sample]]
+* [[IsSampleEvalMode]]
+* [[Certain]]
+* [[Statistical Functions and Importance Weighting]]
+* [[Evaluate]]
+* [[Objects and Values]]