This is more of a historical question: who invented the notation $\perp \!\!\! \perp$ for denoting (conditional) independence?

  • 5
    $\begingroup$ To whom it may concern, this question seems to be on-topic. We have many questions on (history of) notation in probability & statistics, and a tag for them notation. $\endgroup$
    – Tim
    Dec 6, 2018 at 8:07
  • $\begingroup$ So the tiny orthogonal vectors ⊥ mean marginal independence and with two vertical lines it's conditional independence? $\endgroup$
    – suckrates
    Dec 6, 2018 at 8:15

1 Answer 1


I have often seen it associated with AP Dawid 1979, "Conditional Independence in Statistical Theory." For example page 373 of these notes. I have no idea if Dawid actually invented it or popularized it.

Update 8/17/19: According to Wikipedia, the symbol was introduced by Elfving: "Elfving introduced the statistical symbol for probabilistic independence ⊥⊥, which is a stronger condition than orthogonality ⊥, by the 1950s."

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    $\begingroup$ In the 'handbook of graphical models' by Maathuis ea it is written explicitly by Milan Studeny "The author of this chapter was told that the conditional independence symbol $\perp \!\!\! \perp $ was proposed by Dawid and Mouchart in their discussion in the late 1970s" $\endgroup$ Dec 12, 2018 at 11:32

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