Our Savage-Dickey paper has been rejected by the Annals of Statistics, for being too obscure. I completely understand the Editor’s perspective that this resolution of ours has very little bearing on statistical practice and on the community as a whole (“the readership at large”, as I used to write for Series B). But I fear both screeners have missed the main point of our paper which is that papers and books using the Savage-Dickey ratio all start with an assumption that does not make sense from a measure-theoretic point of view… One screener argued that our point is moot, given that everyone agrees on the same version of the density, as otherwise “would even a likelihood function be properly defined?” But this is not true: a likelihood
is the value of the density at the observed value of the random variable. Since this observed value is by nature random, it is not possible to define a specific version of the density function at x… This may alas be related with the progressive disappearance of measure-theory from the Statistics programs: when my third year exchange students go abroad, it is rarer and rarer to find a place that offers Measure Theory at a level lower than a PhD course.