Likelihood notation

by Nate Soares Jul 4 2016 updated Jul 7 2016

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).$~$

[fixme: Make this a child of 'likelihood' when 'likelihood' exists.]