Basic Examples (4) 

Start with a categorical distribution:

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Condition that distribution on the first dimension taking on a value of "A":

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Find the probabilities from that categorical distribution conditioned on the second dimension taking on a value of "E":

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Use a list of patterns instead of rules to impose the same condition as above:

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Scope (3) 

Patterns used in the conditions can be complex:

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The first category must be a letter in the word "ABLE":

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A CategoricalDistribution of arbitrary dimension works with the function:

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The function works with univariate categorical distributions returning a CategoricalDistribution with potentially fewer categories:

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Options (2) 

The value of the "FlattenUnivariate" option (True by default) determines whether the result of a univariate ConditionalCategoricalDistribution has its categories described without a List wrapper:

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Setting the "Marginalize" option to False preserves the dimensionality of the original distribution:

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Applications (2) 

Here is the joint distribution of persons in group A or B who have or do not have some disease, and to whom a test classifies as negative or positive for the disease. Find the joint distribution of persons in group A with respect to disease and test result:

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Find the probability that a person in group A who tests positive is actually sick:

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Compute the fractions of true positives (sensitivity), true negatives (specificity) and false positives (1-specificity) for a mixture of categorical distributions:

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Properties and Relations (1) 

The resource function MixtureCategoricalDistribution increases the dimensionality of a CategoricalDistribution, whereas ConditionalCategoricalDistribution reduces the dimensionality:

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Neat Examples (4) 

The following application comes from the field of causal inference, which is sometimes referred to as "do-calculus". Assume the joint probability distribution of the size of a kidney stone, the treatment one receives for it and how the outcome of that treatment is distributed as set forth below:

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Compute the probability of a good outcome conditioned on the treatment. It will appear that B has better outcomes than A:

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Now synthesize a randomized controlled trial and derive the interventional distribution when one forces the treatment to be "A" by computing a MixtureCategoricalDistribution over stone size in which the components are the conditional categorical distributions based on the stone size and the treatment being A:

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Do exactly the same thing but force the treatment to be "B":

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Although the observational distribution might suggest treatment B is superior, in fact, treatment A is superior and the observational distribution is distorted by the fact that small kidney stones, which generally have better outcomes, are more frequently treated with treatment B.