## a glaring mistake

**S**omeone posted this question about Bayes factors in my book on Saturday morning and I could not believe the glaring typo pointed out there had gone through the centuries without anyone noticing! There should be no index 0 or 1 on the θ’s in either integral (or indices all over). I presume I made this typo when cutting & pasting from the previous formula (which addressed the case of two point null hypotheses), but I am quite chagrined that I sabotaged the definition of the Bayes factor for generations of readers of the Bayesian Choice. Apologies!!!

November 28, 2018 at 10:52 am

À moins que je n’aie jamais rien compris à ce que me racontait mon professeur de mathématiques de Terminale, les $\theta_0$ et $\theta_1$ de la seconde ligne sont des variables dites muettes (puisqu’on intègre dessus), sans signification hors de l’expressin d’intégration. Leur nom n’a aucune importance, qu’on les appelle $\theta$, t voire Jules… Il ne s’agit donc pas vraiment d’une erreur, juste d’une inélégance (encore que…).

Unless I’m severely mistaken, the $\theta$ variables in the second expression are just a notation for designating the variable one integrates upon. These names are therefore arbitrary : call them $\theta$, t, or WhateverYouWish, the meaning will be the same. So this isn’t really a mistake, just an awkwardness (thich, BTW, could be defended as a clarificatin…).

November 28, 2018 at 11:16 am

Second comment on the same theme: I should have written f with indices 0 and 1 then…! Which is not the typo what the reader was rightly confused about.

November 28, 2018 at 7:09 pm

Just to be 200% clear with Ed & Emmanuel, the above integral includes both sets on which the integrals are computed so the ratio.is.not.one! This should be clear as well from my X validated answer.

November 28, 2018 at 12:25 am

Hi Christian!

Without the subscripts, wouldn’t the BF = 1?

– Ed

November 28, 2018 at 9:55 am

Sorry, Ed, I am not sure I get the question right. Do you mean that the sampling densities should be indexed by 0 and 1 as well? I think it is a matter of convention, the model index being part of the parameter vector, even though using the indices would certainly improve clarity. But note that the two integrals are over two different subsets. Thanks!