Conditional dependence

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In probability theory, conditional dependence is the relationship between two or more events that depend when the third event occurs. For example, if A and B are two events that individually increase the likelihood of the third event C , and do not directly affect each other, then initially (when it has not been observed whether or not the C event occurs)

${\ displaystyle {\ text {P}} (A \ mid B) = {\ text {P}} (A) {\ text {and}} {\ text {P}} (B \ mid A) = {\ text {P}} (B)}$ ( A and B are independent).

But suppose now C is observed to occur. If a B event occurs the chance that the occurrence of the B event will decrease as a positive relationship with C is less necessary as an explanation of the event. from C . (Similarly, A event that occurs will decrease the likelihood of occurrence of B ). Therefore, now two events A and B are conditionally negative depending on each other because the probability of each occurrence negatively depends on whether the other is happening. We have

${\ displaystyle {\ text {P}} (A \ mid C, B) & lt; {\ text {P}} (A \ mid C).}$

The conditional dependence differs from the conditional dependence. In conditional independence two events (which may be dependent or not) become independent given the occurrence of the third event.

Video Conditional dependence

Example

Basically, probabilities are influenced by one's information about the probability of occurrence of an event. For example, let the A event be 'I have a new phone'; show B to 'I have a new clock'; and the C event becomes 'I'm happy'; and suppose having a new phone or a new clock increases my chances of happiness. Let's assume that the C event has occurred - which means 'I'm happy'. Now if someone else sees my new watch, he'll reason that my chances of being happy are increased by my new watch, so there's less need to connect my happiness with a new phone.

To make the sample more numerically specific, suppose that there are four possible circumstances, given in the four columns of the following table, where the occurrence of A is indicated by 1 row A and not occurs marked with 0 (as well as for B and C ):

Source of the article : Wikipedia