Talk:Sufficient statistic

message: hello every body
i want to discuss sufficent statistics here... any body has any good information and know the usage of sufficnet stats.. may discuss here... 
thanx
:Do you have specific questions? Michael Hardy 19:53, 7 May 2005 (UTC)
thread_title:  General question 

message: The two examples have h(x)=1.  It might be better if at least one of them did not.  --Henrygb 17:43, 23 May 2006 (UTC)
replies: text: I agree.  An i.i.d. sample from a Poisson distribution would do it.  I'll be back.... Michael Hardy 23:40, 23 May 2006 (UTC)
thread_title: Examples

message: Hello wiki people.
Hopefully, you agree that this page needs some work. I didn't understand it at all and referred to a book instead. What I found was the following information theoretical definition:
The following is a quote directly from copyrighted material: Elements of Information Theory: Thomas M. Cover, Joy A. Thomas:
(begin quote)
This section is a sidelight showing the power of the data processing inequality in clarifying an important idea in statistics. Suppose we have a family of probability mass functions ${f_{\theta}(x)}$ idexed by $\theta$, and let X be a sample from this family. Let T(X) be any statistic (function of the sample) like the mean or the sample variance. Then $\theta\rightarrow X\rightarrow T(X)$ (the notation for a Markov chain) and by the data processing inequality, we have:
I(\theta; T(X)) \le I(\theta; X)
for any distribution on \theta, However, if equality holds, no information is lost. A statistic is called sufficient for $\theta$ if it contains all the information in X about $\theta$
Definition: A function T(X) is a sufficient statistic relative to the family ${f_{\theta)}$ if X is independent of $\theta$ given $T(X)$. i.e. $\theta\rightarrow T(X) \rightarrow X$ forms a Markov chain.
This is the same as the condition for equality in the data processing inequality:
I(\theta, X) = I(\theta, T(X))
(end quote)
I am not a statistician so I'm reluctant to change anything. Please tell me what you think, and just kick my ass if I'm not supposed to put copyrighted material on the talk page.
Jelmer Wind 
:The majority of the article is just a technical proof that a certain method for identifying a sufficient statistic actually works.  The merit of the proof's inclusion and quality of its exposition can be debated; the result of the proof is a very fundamental and important concept for the article.  
:However, the material you quoted is in some sense more complicated than what is already in the article, e.g., the article does not mention Markov chains which is a nontrivial concept.  The quoted def, up to the Markov chain reference, is essentially identical to the one here.  The sentence immediately preceding Thomas's def is essentially the same as the second paragraph in the head.  Both expositions are slightly longer here, but that is almost solely due to much less reliance on technical notation.  The new information from Thomas would be the formulations as a Markov chain and as a data processing inequality.  But their inclusion would also require additional background or wikilinks, so it it not clear to me it would make the article more readable.  
:About the copyright: I am no expert on such, but I do not think the quote here in Talk for purposes of discussion is problematic.  However, incorporation of a quote that long, even if sourced, into the main article probably would be.  But my $0.02¢; others may know better than I.   Baccyak4H (Yak!) 15:01, 18 June 2007 (UTC)
thread_title:  Elements of Information Theory comparison 

message: The proof now dominates most of the article. I think it is now worthy of its own article. Any thoughts? —3mta3 (talk) 14:33, 3 June 2009 (UTC)
replies: text: I think "not yet". I think a major problem with the article is that it does not explicitly deal with nuisance parameters. It would be good to get these added into the general notation in a useful way (but not necessarily everywhere) and to have a statement of "factorisation" that does explicit show in which terms nuisance parameters would appear. It might be best to have a statement of a factorisation theorem that does show nuisance parameters explicitly. If this is so, it might be best to edit the stuff here first and then move the theorem into a separate article. Melcombe (talk) 10:47, 4 June 2009 (UTC)

text: Also, what about renaming the article sufficient statistic, as this avoids the parenthesis in the title? —3mta3 (talk) 07:56, 7 July 2009 (UTC)
replies: text: This is a good idea. The current name is a good dictionary name for the article but sufficient statistic is a better name for this encyclopedia article. PDBailey (talk) 13:27, 7 July 2009 (UTC)
replies: text: I agree that the rename is good, as well that the factorization should not be split out, at least at this time.  Baccyak4H (Yak!) 13:50, 7 July 2009 (UTC)

text: I was partly referring to the connection to ancillarity. But also about clarifying the definition of sufficiency (and the whole article in general) to make it clear what happens for vector parameters ... maybe nothing too special, but the article does start off with "a parameter" and moves onto "the parameter". There are then questions of what happens to the sufficient statistic if a subset of parameters is known... the two-parameter normal distribution is a fairly standard example for this. As for renaming, I think that there needs to be more in an explicity-titled section on the uses of the idea of "sufficiency" or "sufficient statistic" and this might then push for one of the possible names. These uses should include the possible use of sufficency in Bayesian statistics as, besides the standard analytically tracticable cases, the idea can lead to computational savings in MCMC approaches. Melcombe (talk) 15:48, 7 July 2009 (UTC)
thread_title:  Move factorization theorem to new article? 

message: Minimal sufficiency is a fundamental concept just as Completeness (statistics) has its own article. I see a similar suggestion was made to "factorization theorem" (which I think also deserves its own article), but that discussion seemed to have stopped in 2009. Thoughts? Tal Galili (talk) 20:39, 10 November 2014 (UTC)
thread_title:  Move Minimal sufficiency to new article? 

message: Currently we find the following and many similar things in this article:
 Thus the requirement is that, for almost every x,
:\Pr(\theta\mid X=x) = \Pr(\theta\mid T(X)=t(x)).  
The requirement should say something about the probability distribution of θ given X = x or given T(X) = T(x). And note the change from capital T to lower-case t. There is a reason why one distinguishes between capital X and lower-case x; it is as if someone thought that that same reason applies here. To think that is to be unaware of what is being said. This article has dozens of notational crudities like this. I will be back to work on those from time to time. Michael Hardy (talk) 19:37, 25 November 2018 (UTC)
thread_title:  Notational crudities 

message: https://math.stackexchange.com/a/146242/984376 would be great in the article Biggerj1 (talk) 19:34, 19 May 2024 (UTC)
thread_title:  Example Insufficient Statistic