Conditional CategoricalDistributions?

Seth J. Chandler

Here' s a categorical distribution of 3 variables.

In[]:=

cd=CategoricalDistribution[{{"A","B","C"},{"α","β"},{"☺","☹"}},{{{6,84},{8,48}},{{63,91},{88,78}},{{34,72},{74,55}}}]

Out[]=

CategoricalDistribution

Input type: Vector (length: 3)

Categories:

A

B

C

×

α

β

×

☺

☹



Suppose what I want now, however, is a conditional probability distribution represented -- and this is crucial -- as a CategoricalDistribution, in which I look only at Group A. How do I do this?

Here' s some ugly code that accomplishes my goal.

In[]:=

conditionalDistribution[cd_CategoricalDistribution,outerlevel_]:=CategoricalDistribution[Rest@Information[cd,"Categories"],Normal@Query[outerlevel,Values,Values][Information[cd,"ProbabilityTable"]]]

In[]:=

condcd=conditionalDistribution[cd,"A"]

Out[]=

CategoricalDistribution

Input type: Vector (length: 2)

Categories:

α

β

×

☺

☹



In[]:=

Information[condcd,"ProbabilityTable"]

Out[]=

	☺	☹
α	3/73	42/73
β	4/73	24/73

But, surely, I say, there is a better (and more general) way?