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
See Also