Conditional independence

conditional independence

If, for each value of the variable C, the variables A and B are independent of one another, then they are said to exhibit conditional independence. If the variables are categorical, with p_jkl denoting the probability of an outcome in cell (j, k, l), then A and B are conditionally independent, given the category of C, if and only if

,

for all j, k, and l, where p_j0l=∑_kp_jkl, p_0kl=∑_jp_jkl, and p_00l=∑_j∑_kp_jkl.

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A Dictionary of Statistics. Second edition revised. Copyright © Oxford University Press, 2008. All rights reserved.

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