# Likelihood notation

The likelihood of a piece of evidence \(e\) according to a hypothesis \(H,\) known as “the likelihood of \(e\) given \(H\)”, is often written either \(\mathcal L_e(H)\) or \(\mathcal L(H \mid e).\) The latter notation is confusing, because then \(\mathcal L(H \mid e) = \mathbb P(e \mid H).\) Many students of statistics find it hard enough to keep the difference between \(\mathbb P(H \mid e)\) and \(\mathbb P(e \mid H)\) straight in their heads if we *don’t* occasionally swap the order of the arguments when talking about similar functions, so on Arbital, we much prefer the notation \(\mathcal L_e(H) = \mathbb P(e \mid H).\)

Make this a child of ‘likelihood’ when ‘likelihood’ exists.

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