empirically Bayesian [wISBApedia]
Last week I was pointed out a puzzling entry in the “empirical Bayes” Wikipedia page. The introduction section indeed contains a description of an iterative simulation method that involves an hyperprior p(η) even though the empirical Bayes perspective does not involve an hyperprior.
While the entry is vague and lacks formulae
These suggest an iterative scheme, qualitatively similar in structure to a Gibbs sampler, to evolve successively improved approximations to p(θ∣y) and p(η∣y). First, calculate an initial approximation to p(θ∣y) ignoring the η dependence completely; then calculate an approximation to p(η | y) based upon the initial approximate distribution of p(θ∣y); then use this p(η∣y) to update the approximation for p(θ∣y); then update p(η∣y); and so on.
it sounds essentially equivalent to a Gibbs sampler, possibly a multiple try Gibbs sampler (unless the author had another notion in mind, alas impossible to guess since no reference is included).
Beyond this specific case, where I think the entire paragraph should be erased from the “empirical Bayes” Wikipedia page, I discussed the general problem of some poor Bayesian entries in Wikipedia with Robin Ryder, who came with the neat idea of running (collective) Wikipedia editing labs at ISBA conferences. If we could further give an ISBA label to these entries, as a certificate of “Bayesian orthodoxy” (!), it would be terrific!
Xi'an's Og 
August 9, 2021 at 11:15 am
« If we could further give an ISBA label to these entries, as a certificate of “Bayesian orthodoxy” (!), it would be terrific! »
… and terrifying to anybody remembering what the “orthodoxy” concept (and more generally the innumerable variants of authority principle) did to science in various settings.
Heuristically, “I tell you so” should be treated as a flag for flaky argumentation. Isn’t there a better way ?
August 11, 2021 at 10:58 am
Indeed, where there are certificates of orthodoxy the inquisition can’t be far behind.
August 11, 2021 at 8:44 pm
Sorry Roger, this was a tongue-in-cheek sentence, obviously lost in translation! I am merely interested in a collaborative on-site improvement over the Bayesian entries in Wikipedia during our bi-annual meeting, next year in Montréal. Orthodoxy does not appeal to me either…
August 11, 2021 at 8:49 pm
OK, sorry for attempting double-talk with no preliminary warning!!!
August 12, 2021 at 9:48 am
No worries, your original comments about Gibbs seem well taken. The Bayes/empirical Bayes boundary is obviously quite porous and this seems to me to be a Good Thing, enabling travel across it without excessive paperwork, unlike what Brexit has wrought on the UK.
August 9, 2021 at 1:53 am
I think that’s a good idea. Although many of the statistical references at Wikipedia are useful and good, some have holes, like many of the technical subjects. Some are incomplete. Some confound different subjects. “Bayesian hierarchical model” maps to “Bayesian network” but “Bayesian hierarchical modeling” has its own page, even if that page is incomplete — no connection to multi-level models, for instance — and I dislike its second paragraph. Under “Bayesian network” there is one mention of Bayesian hierarchical model but no cross-reference to “Bayesian hierarchical modeling.” Moreover, they don’t mention the chain rule in this connection, and the treatment of a nuisance parameter in its “statistical introduction” is at least confusing.
From the little experience I have had trying to influence the content of other pages, though, one problem is that Wikipedia editing has a style or set of rules that’s grown up with it, mostly ones which guide editing of qualitative subjects. It might help for ISBA to coordinate with Wikipedia editors with ISBA being Experts On The Subject.