Talk:Bayesian information criterion

message: I would like to add the following comment for the limitations:
# the BIC relies on a local approximation of the posterior moments, based on the assumption that the mode of the posterior probability is close to the expected value of the parameters of the model , Raftery AE. "Bayesian Model Selection in Social Research.", Sociol Methodol 1995;25:111. doi:10.2307/271063.. For skewed posteriors, this approximation might not hold.
Would anyone argue with that? 
MickeyMoens 05:56, 12 November 2016 (UTC)
thread_title:  Local approximation 

message: As far as I know, SC and BIC are different. What is described is BIC.
:The formula given matches that derived by Schwarz (1978)
:There does some to be some confusion here though, as e.g. Bengtsson and Cavanaugh define SIC as given here, and BIC differently.
:Can anyone provide some authoritative references to the modern use of the terms BIC and SIC?
:--Ged.R 15:18, 22 January 2007 (UTC)
replies: text: Should "SIC" in the first formula be "BIC"? The acronym "SIC" is never defined in the article.
The first formula is bizarre. geez. "The formula for the BIC is exp(-SIC/2) ???" What's up with that?
The entire article sounds like it is written by wannabe experts who aren't exactly certain of what they're talking about. Read this from the perspective of someone who is trying to ascertain the basic formula for BIC. (That is my situation. I have a software package that purports to calculate AIC and BIC scores but it (the software package) doesn't say exactly what it is calculating. Neither does this article. It introduces all these terms, xbar, etc and never says what they are. A "constant becoming trivial" is a pretty weird notion if you ask me. This could potentially be a very important article as statistical model selection invades more and more fields but as it currently is it is useless as a first approximation. You should keep the constants that become trivial. An article written by people who know this stuff, sort of, for people who also sort of know this stuff is useless.   —Preceding unsigned comment added by 67.0.90.202 (talk) 23:42, 3 January 2011 (UTC)

text: 81.231.127.12 (talk) 22:09, 18 December 2010 (UTC)
replies: text: I've just reverted a change to that first formula that was made on 15 November, so it now agrees with the reference given and the standard definition of BIC. I agree that this article is in need of attention but this is not my area of expertise so I'll flag it as in need of expert attention from a suitable statistician. Thanks for pointing this out. To be honest I'm surprised the article was left like this for over a month. Qwfp (talk) 09:58, 4 January 2011 (UTC)
replies: text: A problem is that it is unclear what source is actually being used for any of these formula. For example,  the Priestley reference has a different formula for BIC than that for which it is supposedly being used as a source. But it does give formulae relating AIC, SIC and BIC all within the same context. It seems that Priestley uses S (here SIC) for what is here called BIC, and has a rather more complcated formula for his BIC. Thus Priestly uses BIC for "Akaike's BIC", and S for Schwarz's criterion ("Schwarz's BIC" although he doesn't call it that), where Schwarz's criterion is what is here called BIC. So a first question is what are good sources for current terminology, and is there a consistent usage? The above discussion mentions "the standard definition of BIC" ... are there good sources for such a thing. Melcombe (talk) 16:08, 5 January 2011 (UTC)
thread_title:  SIC vs BIC 

message: The version of BIC as described here is not compatible with the definition 
of AIC in wikipedia. There is a divisor n stated with BIC, but not AIC in the Wikipedia 
entries. It would save confusion if they were consistently defined! 
I would favour not dividing by n: i.e. 
BIC = -2log L + k ln(n)
AIC = -2log L + 2k
One can then clearly compare the two, and see they are similar for
small n, but BIC favours more parsiminious models for large n. —The preceding unsigned comment was added by 128.243.220.42 (talk) 13:47, 10 May 2007 (UTC)
thread_title:  This formula for BIC may potentially confuse people who read the AIC entry.  

message: Hi,
Is L in the formula for the BIC really the log-likelihood?  It seems to me that L is the likelihood, s.t. ln L would be the log-likelihood and the -2 ln L term is the same term as in the AIC.  Am I missing something?
Mpas76 01:05, 17 October 2007 (UTC)
thread_title:  Definition of L 

message: Possibly I haven't understood this properly, but surely the formula for so-called 'error variance' in the article is wrong:
\hat{\sigma_e^2}=\frac{1}{n}\sum_{i=1}^n (x_i-\overline{x})^2
If the x's are datapoints this appears to be the variance of the datapoints, whereas what we want is something like the RSS of the AIC article, presumably the mean squared error:
\hat{\sigma_e^2}=\frac{1}{n}\sum_{i=1}^n (x_i-\hat{x_i})^2
93.96.236.8 (talk) 16:42, 11 September 2010 (UTC)
thread_title: Error variance

message: The article explicitly mention that the investigated model should be a member of the exponential family. This was the original assumption in the demonstration of BIC assymptotical property. However, the derivation of this property was extented to less restrictive conditions. For example Cavanaugh and colleague in “Generalizing the Derivation of the Schwarz
Information Criterion”  —Preceding unsigned comment added by 195.220.100.11 (talk) 18:11, 4 March 2011 (UTC)
thread_title:  Exponential family 

message: Has anybody notice that minimization of the objective function:
:{-2 \cdot \ln{p(x|k)}} \approx \mathrm{BIC} = {-2 \cdot \ln{L} + k \ln(n) }. \ 
seems to lead to a penalty on larger data sets.
For example, given a data set D1, and another nested data set D2 (same features, but a subset of samples of D1). BIC seems to suggest that D2 should have more parameters than D1. This is ridiculous.             147.8.182.107 (talk) 05:02, 8 January 2012 (UTC)
thread_title: BIC penalizes larger data set?

message: The source for the sentence "Akaike was so impressed with Schwarz's Bayesian formalism that he developed his own Bayesian formalism, ..." does not actually support that statement. The source is from 1977, Schwarz's work is from 1987. 
Are the facts maybe twisted here? What is clear is that Akaike developed the AIC before Schwarz developed the BIC (1974 vs.1978). Schwarz also cites Akaikes work in his 1978 paper. Is ABIC different from AIC and if yes, how? Can someone please add a correct source?
Georg Stillfried (talk) 14:07, 2 August 2013 (UTC)
thread_title:  Akaike impressed? 

message: It would be good to keep notation's consistent between this page and the AIC page.
For instance, consider:
:\mathrm{AIC} = 2k - 2\ln(L)
versus
: \mathrm{BIC} = {-2 \cdot \ln{\hat L} + k \cdot \ln(n)}. \ 
There is a hat in the likelihood, \cdot is being used, and the order of the factors is inconsistent too Ric8cruz (talk) 17:47, 1 November 2015 (UTC)
thread_title:  Notation Consistency 

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