# 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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