# Bayesian Revision (Command Program)

DPL automatically performs any Bayesian revisions necessary to calculate probabilities. The following command requires a Bayesian revision (because event MarketShare depends on event Competition).

`Competition | MarketShare;`

The Session Log displays two probability distributions, one for each state of conditioning event MarketShare. (Command | Execute | Formulas is turned off.) Because Competition can assume two states, each distribution consists of two probabilities (See Displaying Probability Distributions).

```Competition | MarketShare
~~~MarketShare.Gain
___Competition.Strong: 0.533333
___Competition.Weak: 0.466667

~~~MarketShare.Lose
___Competition.Strong: 0.914286
___Competition.Weak: 0.0857143
```

With Command | Execute | Formulas turned on, you can see how DPL performs the Bayesian revision.

```Competition | MarketShare

~~~MarketShare.Gain

>>>>>>>>>>>>> FORMULAS (numerators)

___Competition.Strong
(MarketShare.Gain | Competition.Strong) * Competition.Strong
___Competition.Weak
(MarketShare.Gain | Competition.Weak) * Competition.Weak

>>>>>>>>>>>>> PROBABILITIES

___Competition.Strong: 0.533333
___Competition.Weak: 0.466667

~~~MarketShare.Lose

>>>>>>>>>>>>> FORMULAS (numerators)

___Competition.Strong
(MarketShare.Lose | Competition.Strong) * Competition.Strong
___Competition.Weak
(MarketShare.Lose | Competition.Weak) * Competition.Weak

>>>>>>>>>>>>> PROBABILITIES

___Competition.Strong: 0.914286
___Competition.Weak: 0.0857143
```

In the output to the Log, notice that the formulas are listed as numerators. In Bayesian revisions, the denominator is the sum of the numerators for each event state.

In another example, the states of both the conditioned event and the conditioning event are specified.

`Competition.Strong | MarketShare.Gain`

The Log displays a single probability output.

```Competition.Strong | MarketShare.Gain
(MarketShare.Gain | Competition.Strong) * Competition.Strong
------------
Competition.Strong * (MarketShare.Gain | Competition.Strong)
+ Competition.Weak * (MarketShare.Gain | Competition.Weak)
: 0.533333
```

Note that because only one state of the conditioned event was requested, the resulting formulas contain both the numerator and the denominator, presented as a fraction.

In the next example, the state of the conditioning event is not specified.

`Competition.Strong | MarketShare`

The Log displays two probabilities, one for each state of conditioning event.

```~~~MarketShare.Gain
(MarketShare.Gain | Competition.Strong) * Competition.Strong
------------------
Competition.Strong * (MarketShare.Gain | Competition.Strong)
+ Competition.Weak * (MarketShare.Gain | Competition.Weak)
: 0.533333

~~~MarketShare.Lose
(MarketShare.Lose | Competition.Strong) * Competition.Strong
------------------
Competition.Strong * (MarketShare.Lose | Competition.Strong)
+ Competition.Weak * (MarketShare.Lose | Competition.Weak)
: 0.914286
```

Versions: DPL Professional, DPL Enterprise, DPL Portfolio