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Why is conditional independence more useful than full independence?

  • A.It guarantees that the joint distribution is uniform
  • B.It holds far more often while still permitting factorisation
  • C.It is easier to verify from data than full independence
  • D.It applies to continuous variables where independence does not

Answer: B

Interesting variables are rarely independent, but very often become so once a common cause is known, and that is enough to factorise the joint into small pieces. Verification is not easier, continuity is irrelevant and uniformity does not follow. Finding the weakest assumption that still delivers the structural benefit is a recurring move, and here it is what makes probabilistic reasoning over many variables possible at all. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

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