Talk:Empirical Bayes method

message: As far as I understand from the modern Bayesian perspective empirical Bayes is about hierarchical Bayesian models and learning the parameters of a prior distribution by sharing that distribution across different data sets. In other words it is an assumption that these data sets are conditionally independent given the prior parameters. I don't detect any of that in this article. Am I missing the point or something?
:I don't see how you're failing to detect it.  Look at the quantity called Θ in the article. Michael Hardy 22:44, 30 July 2006 (UTC)
thread_title: Data sets are conditionally independent given the prior parameters

message: In the introduction part, I understands most of them until the sentence
"Empirical Bayes then employs the complete set of empirical data to make inferences about the prior θ, and then plugs this into the likelihood ρ(y | θ) to make estimates for future outcomes of individual measurements."
First of all, what kind of estimation won't use the "complete set of empirical data"? I am not an expert in Statistics, so forgive me if I am ignorant. As far as I knew, for estimation, it is always better to use the entire dataset, except that you are talking about cross-validation.
Secondly, what do you mean of "plugs this estimation into the likelihood"? It would be better to write it in a mathematical equation about the statement. I am guessing you are saying that one predicts new data y_new by p(ynew|yold)=p(ynew|\theta)p(\theta|yold). Is it correct?  —Preceding unsigned comment added by 76.121.137.101 (talk) 10:23, 18 February 2008 (UTC)
thread_title:  Some confusions 

message: This article should be re-written. I submit that it is way over the head of most Wikipedia readers. The Gunning Fog Index of the Introduction paragraph is over 19, indicating a post-graduate education is needed to understand it. The introductions should explain the basic concept to the average reader, even if the particulars are too technical.
I came to this article because Empirical Bayes is becoming common in highway safety research, but despite 3 years of math in college, and 16 years experience as a traffic engineer, I learned nothing from this article.--Triskele Jim (talk) 18:08, 8 January 2009 (UTC)
replies: text: Agreed. I tried to write a short, to-the-point intro.  —Preceding unsigned comment added by 84.238.115.164 (talk) 17:35, 20 February 2010 (UTC)
thread_title:  Clarity 

message: The famous James-Stein estimator (the classic example of a shrinkage estimator) for the mean of a Gaussian has its theoretical foundation in empirical Bayes. It results from applying empirical Bayes to the estimation of the covariance matrix of a Gaussian prior with fixed mean zero. The JS estimate is simply the Bayes estimator for the resulting posterior. Would be interesting to add a section about this.  —Preceding unsigned comment added by 84.238.115.164 (talk) 17:17, 20 February 2010 (UTC)
thread_title:  Shrinkage/James-Stein estimators 

message: [This is my first post. Please be forgiving]
The term "Empirical Bayes" is used in many contexts with many different meanings. A short review is suggested in I. J. Good, “Introduction to Robbins (1955) An empirical Bayes approach to statistics,” Breakthroughs in Statistics: Foundations and basic theory (1992): 379.  
In a nutshell, it was originally used in an estimation problem with a physical (frequentist, non epistemic), non-parametric prior distribution. Soon enough it started being used for "pseudo-Bayes" problems with a parametric prior, and even for pure Bayes (epistemic/De Finetti prior) with a composite parametric prior, despite the original EB was purely frequentist.
I believe emphasis should be put on the frequentist nature of the "original" empirical Bayes, versus it's epistemic spin offs. 
<John.ros 17:15, 8 February 2011 (UTC)
replies: text: What does epistemic mean in this context?  As for what the article should focus on, I'd say that the essence of Empirical Bayes is that it is a frequentist's approach for selecting the hyperparameters that determine a Bayesian's prior distribution for the parameters.  —Quantling (talk | contribs) 14:20, 10 February 2011 (UTC)
replies: text: By "epistemic" I mean subjective prior. I.e.- the prior describes my beliefs and not the relative frequencies in some hyper-population. John.ros (talk) 15:50, 12 February 2011 (UTC)
thread_title: Original meaning of the term

message: There seems to be an error (or simply poor notation) in the final example.  In particular, the example is using y as the full data, but the posterior is apparently only using 1 data point.  Then the final bayes estimator includes ybar, but this is only correct for a sample of size one.  For a sample of size n, the estimator should be \frac{n \bar y + \alpha}{n+1/ \beta}.
I'd make the change myself, but it would almost surely be reverted before anyone even looks at the change.  — Preceding unsigned comment added by 130.113.126.119 (talk) 18:45, 31 July 2012 (UTC)
thread_title: Error in Poisson-Gamma model