Timeline for What are these "hyper-distributions" called?
Current License: CC BY-SA 3.0
11 events
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| Jul 10, 2018 at 0:40 | history | edited | kjetil b halvorsen♦ |
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| Sep 24, 2015 at 12:12 | comment | added | Guillaume Dehaene | I'd rather avoid that notation completely and use "parameter" random variables conditional on which x has a specific distribution. So in your example, I would say there is a random variable $\alpha$ such that $p(x|\alpha=1)=p_1(x)$ and $p(x|\alpha=2)=p_2(x)$ (and then specify an ordinary probability distribution on $\alpha$) | |
| Sep 24, 2015 at 3:24 | comment | added | user157969 | @GuillaumeDehaene Thanks! I will read. Any ideas for a better name? | |
| Sep 23, 2015 at 10:23 | comment | added | Guillaume Dehaene | I've seen similar notation used in this arxiv paper arxiv.org/abs/1308.6306 where they refer to it as a "prior" distribution. I'm not a fan of the name however | |
| Sep 22, 2015 at 5:02 | comment | added | user157969 | @user777 Thanks, yes I think you on the right track - in fact what I am thinking of could be described as a "nonparametric hyperprior". | |
| Sep 22, 2015 at 3:38 | comment | added | Sycorax♦ | I'm not sure if this applies, but it sounds a lot like what goes on in a Bayesian hierarchical model where we have some data distributed as some distribution, but at least some of those parameters are unknown, so we place a prior over the parameters themselves and the model has several layers. | |
| Sep 22, 2015 at 3:13 | comment | added | user157969 | @whuber Apologies about the description, I have added some more detail. I am interested in the former of the two options you describe ("probability distribution over the set of all univariate distribution functions"). They are indeed some kind of Bayesian prior distribution, but I am looking for a more specific term I can search for :) | |
| Sep 22, 2015 at 3:12 | history | edited | user157969 | CC BY-SA 3.0 |
Replaced "value" with "realization". Added notation for Q. Added "edit" section. Added dirichlet-process tag.; deleted 1 character in body
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| Sep 21, 2015 at 14:18 | comment | added | whuber♦ | Are you perhaps referring to a (Bayes) prior distribution? Your description is not clear, because "assign a second probability measure to the set of all possible values of the pdf $p$" could be interpreted liberally, in the sense of a probability distribution over the set of all univariate distribution functions, or literally, in the sense that identifies "all possible values" with $\mathbb R$. Which is it? | |
| Sep 21, 2015 at 4:57 | comment | added | John Jiang | I think you are thinking of level set of probability distributions. This paper may be helpful: pelletierb.perso.math.cnrs.fr/Publications_files/cpp-jnps.pdf | |
| Sep 21, 2015 at 4:20 | history | asked | user157969 | CC BY-SA 3.0 |