# Conditional Dependence Relationship

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A Conditional Dependence Relationship [math]\displaystyle{ CI(A,B,C) }[/math] is a Statistical Relationship that is true if and only if ...

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**Counter-Example(s):****See:**Association, Conditional Independence.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/conditional_dependence Retrieved:2015-2-25.
- In probability theory,
**conditional dependence**is a relationship between two or more events that are dependent when a third event occurs.^{[1]}^{[2]}For example, if*A*and B are two events that individually affect the happening of a third event*C*, and do not directly affect each other, then initially (when the event*C*has not occurred) : [math]\displaystyle{ P(A\mid B) = P(A) \text{ or } P(B\mid A) = P(B) }[/math]^{[3]}^{[4]}(*A*and B are independent) Eventually the event*C*occurs, and now if event*A*occurs the probability of occurrence of the event B will decrease (similarly event B occurring first will decrease the probability of occurrence of*A*in future). Hence, now the two events A and*B*become conditionally dependent because their probability of occurrence is dependent on either event's occurrence. Intuitively we can say that since A and*B*both were probable causes of C*, given*C*has occurred, occurrence of either of A or B alone could explain away the happening of*C*. : [math]\displaystyle{ P(B\mid C) \gt P(B\mid C,A) }[/math]*A be 'I have a new car'; event^{[5]}In essence probability comes from a person's information content about occurrence of an event. For example, let the event*B*be 'I have a new watch'; and event C*be 'I am happy'. Let us assume that the event C has occurred – meaning 'I am happy'. Now if a third person sees my new watch, he/she will attribute this reason to my happiness. Thus in his/her view the probability of the event*A ('I have a new car') to have been the cause of the event*C*('I am happy') will decrease as the event*C*has been explained away by the event*B*. Conditional dependence is different from conditional independence. In conditional independence two events which are initially dependent become independent given the occurrence of a third event.^{[6]}

- In probability theory,

- ↑ Introduction to Artificial Intelligence by Sebastian Thrun and Peter Norvig, 2011 "Unit 3: Conditional Dependence"
- ↑ Introduction to learning Bayesian Networks from Data by Dirk Husmeier [1] "Introduction to Learning Bayesian Networks from Data -Dirk Husmeier"
- ↑ Conditional Independence in Statistical theory "Conditional Independence in Statistical Theory", A. P. Dawid"
- ↑ Probabilistic independence on Britannica "Probability->Applications of conditional probability->independence (equation 7) "
- ↑ Introduction to Artificial Intelligence by Sebastian Thrun and Peter Norvig, 2011 "Unit 3: Explaining Away"
- ↑ Conditional Independence in Statistical theory "Conditional Independence in Statistical Theory", A. P. Dawid