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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