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Conditionally independent data structure

By Independence Test and analyzing the relationship of variables, it is possible to Making Hypothesis by Correlation , but the asymmetry of the structure of the data is not known.

If you look at "conditional independence", you will be able to get the Structure of data that becomes a directed graph .

Relationship between conditional independence and directed graphs

If the variables of the qualitative data A and B are independent, for example, the Contingency Table looks like this: There is not much bias in the frequency.
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If the variables of the qualitative data A and B are independent, and A and B are conditional but independent, for example, the figure below. In this case, the frequency is not too biased.
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If the variables of the qualitative data A and B are independent and A and B are not conditionally independent, for example, the following two examples. In this case, the frequency is biased.
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If conditionally not independent, the directed graph will look like the one below. Since the variables A and B are independent of each other, there is no line between A and B.
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How to comprehensively investigate conditional independence

Structure Analysis by Bayesian Network is designed to comprehensively investigate conditional independence relationships and create directed graphs when there are many variables.






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