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When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$

Where is the no information for the parameter?

and if would be informative prior, Where one would see the 'information' given?

I saw the definition on Wikipedia https://en.wikipedia.org/wiki/Prior_probability and there mentions 'An informative prior expresses specific, definite $\color{blue}{\text{information}}$ about a variable.'

My question is where is this $\color{blue}{\text{information}}$ given in my particular example for instance?

Could you help please?

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marked as duplicate by kjetil b halvorsen, Michael Chernick, Xi'an bayesian Feb 11 at 6:09

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ I don't think this question is a duplicate. The proposed duplicate is asking about the rationale for using informative vs. uninformative priors, whereas this question seems to be asking about how to identify informative vs. uninformative priors. $\endgroup$ – user20160 Feb 11 at 0:02
  • $\begingroup$ @user20160 I don't think this is a duplicate neither. Though I didn't mean to ask how to identify informative vs. uninformative priors. I meant the current questions actually :) . I saw the definitions on Wikipedia en.wikipedia.org/wiki/Prior_probability and there mentions An informative prior expresses specific, definite information about a variable. where is this information given? $\endgroup$ – Isa Feb 11 at 1:17
  • $\begingroup$ @user20160 Your question 'how to identify informative vs. uninformative priors' is an interesting one btw. $\endgroup$ – Isa Feb 11 at 1:20
  • $\begingroup$ @Isa I see. You might consider editing your question to include this. This could help clear up the duplicate issue, and help people understand exactly what you're asking. $\endgroup$ – user20160 Feb 11 at 1:42
  • $\begingroup$ @user20160 I've edited $\endgroup$ – Isa Feb 11 at 2:03