> Also, "empirical Bayes" is in modern parlance equivalent to "Bayes". What's the alternative? "Conjectural Bayes"?
My understanding of the difference, as a frequent user of empirical Bayes methods (mainly limma[1]), is that in "empirical Bayes" the prior is derived empirically from the data itself, so that it's not really a "prior" in the strictest sense of being specified a priori. I don't know whether this is enough of a difference in practice to warrant a different name, but my guess is that whoever coined the term did so to head off criticisms to the effect of "this isn't really Bayesian".
My understanding of the difference, as a frequent user of empirical Bayes methods (mainly limma[1]), is that in "empirical Bayes" the prior is derived empirically from the data itself, so that it's not really a "prior" in the strictest sense of being specified a priori. I don't know whether this is enough of a difference in practice to warrant a different name, but my guess is that whoever coined the term did so to head off criticisms to the effect of "this isn't really Bayesian".
[1]: https://bioconductor.org/packages/release/bioc/html/limma.ht...