# Talk:Bayes linear statistics

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Field: Probability and statistics

## Rewrote Introduction

I rewrote the introduction to bring it closer to the original concept. Let me know if you see any problems.... Now just need to rewrite the rest!!! ;) —Preceding unsigned comment added by 130.102.0.171 (talk) 09:14, 5 November 2009 (UTC)

## Find new name

"Bayes linear" doesn't seem to be a good name for this topic. I won't pretend to understand what is going on, but it looks as if the "linear" bit comes from "linear statistics" in the book title. So, if this article is at all worthwhile, can someone find an appropriate noun to go with and follow the adjective "linear". Melcombe (talk) 16:49, 8 April 2008 (UTC)

I was a student at Durham University and Michael Goldstein was my advisor. I did the module on this subject and we called it "Bayes Linear Statistics", however seeing as the module was by the far the hardest thing I ever did and the author of this page clearly knows far more about it than me, I don't feel confident to change the name of the page. —Preceding unsigned comment added by 91.109.181.223 (talk) 21:53, 15 May 2009 (UTC)

Hi there,

I started this article and then realised I bit off more than I can chew... it is a very hard topic, and the idea is very original which the name "bayes linear" doesn't really convey.. I do agree with the name change to bayes linear statistics, bayes linear analysis might also be used.

I am not wild about having the references to linear regression and particularly where they currently sit in the text. Did Michael Goldstein teach this as part of the Bayes Linear Statistics module? (BTW I am envious that you got to do stats under Goldstein!).

I also think a statement saying that probability theory is a linear theory needs to be made to distinguish between bayes linear statistics and linear regression.

In Revising Previsions: A Geometric Interpretation (Michael Goldstein) Journal of the Royal Statistical Society. Series B (Methodological) 1981 Goldstein quotes de Finetti:

"The pre-eminent - one might say exclusive - role of linearity in the theory of probability theory has always remained very much in the background".... Anyway I think we really need to add a statement like this to clarify the meaning of the title and distinguish from linear regression... maybe the statement that I made was a little sweeping, but I think something needs to be changed there. I quote the article without real understanding of it, it is a bit of a monster...

Maybe one day I will understand these topics well enough to finish the article and add sections on the following:

Temporal sure preference principle

second order exchangeability

bayes linear sufficiency

—Preceding unsigned comment added by 130.102.0.170 (talk) 24 June 2009 (UTC)

I deleted the insertion about probability theory being linear because it does not make sense ... after all, probabilities both multiply together as well as add. The extra reference above is usefull and I have added it to the article. It seems the quote of a quote, quoted above, lost some meaning somewhere ... I think that it is actually taking about linearity of expectations. I admit to having not seen the book, but from the paper and the blurb on the publisher's website it seems that the present article doesn't fully reflect the context of the theory here .... that it works with "previsions" rather than probabilities. Melcombe (talk) 14:42, 24 June 2009 (UTC)

Sorry if the quote of a quote (etc) was confusing...

I think the statement that probability theory is a linear theory is correct, but needs careful justification (which I didn't give). I am pretty sure that "Theory of probability" gives this, but I will need to find it... Expectations/previsions are a generalisation of probabilities i.e. a probability is the expectation of an indicator variable. Multiplication and addition are both linear operations so I think this poses no problem.

You are right there should also be discussion of prevision/expectation early in the article. There is a really good definition in Frank Lad's book which I might add.

Anyway I am glad there is some interest in extending this article even though I have some reservations about some of the edits. I won't reverse them without consulting these sources so that I can really defend the changes I make. This will probably take a while... :)

—Preceding unsigned comment added by 130.102.0.170 (talk) 25 June 2009 (UTC)

I don't know why autosigning of your comments is not working here? But you might try signing them yourself as is supposedly standard.

OK, there may be a way in which the theory of probability might be considered linear, but it is not obvious what is actually meant. As for edits ... the article seemed/seems to lack any structure and had/has no background context. It needs pushing to improve these things. One thought is whether there is a need for a separate article on "prevision" in the sense used in the Goldstein paper ...would it make this article easier to structure, or would they essentially be the same article? This might bring us back to the question of a name for this article. Does the theory supposedly behind "Bayes linear statistics" have any connection to Bayes theorem etc... It may give a rule for updating when probabilities cannot be used, but Bayes' theorem relates to probabilities. So is "Bayes linear statistics" anything more than the title of a book and some associated courses. Does anyone else use this terminology? Melcombe (talk) 08:54, 25 June 2009 (UTC)

I think the article is still at the stub stage... I am not against a complete rewrite at all..

I like the idea of a separate article on prevision...

Goldstein seems to adopt prevision in his earlier work but uses Expectation latter on. Still refering to the existing article on expectation won't really help...

Under some circumstances computing the adjusted expectation is equivelant to bayesian conditioning but it isn't in general. If enough effort is put into a Bayes Linear analysis it will eventually become a traditional Bayesian analysis. However the connection to Bayesian theory is subtle, one of Goldstein's key arguments is that the role of conditioning (by Bayes theorem) is overplayed in the traditional Bayesian paradigm.

The Bayes Linear Theory is still a little embryonic and very original which makes it a difficult topic... It also makes it difficult to draw connections to other articles (e.g. we can't really refer to the existing expectation article, but instead need to write a new one as you suggest called "Prevision").

Bayes linear statistics is on the fringe of traditional bayesian statistics, but I do think it is more than a book and a course. There is a group working on the topic although it might be the case that everybody working on it was at one stage at Duhram University...

Obviously I think it is worthwhile sticking with this as a Wikipedia topic, but I see getting it right as a long term project... For the same reasons that writing this is difficult, it is also beneficial...

Autosign still isn't quite right, but this is who I am: David.Rohde ([User talk:David.Rohde|talk]]) 26 June

## Suggest name-change to "Bayes linear statistics, a book and approach of Michael Goldstein" rather than deletion or status-quo

This article very closely follows Michael Goldstein's work and his recent text (with Wolf), to which leaders of Bayesian statistics have shown great respect.

However, Goldstein's approach and this article may be somewhat idiosyncratic, and the "patenting" (forgive my word-choice, but that's what my brain outputs at this hour)---the "patenting" of the name "Bayes linear statistics" on Wikipedia to describe Goldstein's (important) work is problematic, because of the notable works of other authors, e.g. Box & Tiao, Zellner, Broemling, Drèze, etc. I agree that a name-change or deletion may be worth considering, with my preference strongly favoring a name-change. Kiefer.Wolfowitz (talk) 18:02, 25 June 2009 (UTC)

I am ok with the name change... The name has some wider use but it seems to be nearly exclusively with Duhram university people... It is hard to imagine this name sticking in the longterm... but it isn't really the place of an encylopedia to come up with a name so your suggestions sounds ok. Maybe one day it will be called de Finetti-Goldstien Theory or similar...

I actually would like the article to be marked as a stub as well, but I am not sure how to do this. I would prefer this to deletion... David.Rohde ([User talk:David.Rohde|talk]]) 26 June.

I have marked the article as a stub, but it was not that strongly needed. The name suggested above is too long I think for Wikipedia. I would be interested in details of the other author's work mentioned ... I wonder if it is actually in the same context as here, of not having a fully prescribed prior distribution and just having "linear updating rules", which isn't the same as using improper priors. The work I have seen of Box & Tiao and Zellner was fully within the standard Bayesian approach to regression with fully specified, if sometimes improper, priors. Melcombe (talk) 08:38, 26 June 2009 (UTC)