9

Title says it all.

I have seen both "the hyperparameter of the Dirichlet distribution" and "the parameter of the Dirichlet distribution"

What are the differences?

amoeba
  • 104,745
Sibbs Gambling
  • 2,609
  • 2
    https://en.wikipedia.org/wiki/Hyperparameter – Glen_b Jan 12 '15 at 04:30
  • 2
    See also the answer here – Glen_b Oct 02 '15 at 09:58
  • @Glen_b, it seems that we have three identical threads asking about a definiton of hyperparameter. I suggest to merge (moving the answers) all of them into http://stats.stackexchange.com/questions/208225. But your answer here is accepted and you will lose this green tick if this answer is moved. What do you think? – amoeba May 14 '16 at 18:27
  • @amoeba I don't really mind about the tick. I'll have a closer look at the threads; a certain degree of caution is called for with merging. – Glen_b May 15 '16 at 01:05
  • @Glen_b: Shall I raise this as a suggestion on meta, or is it okay to leave it as a pending flag for the moderators to figure out? – amoeba May 17 '16 at 16:05
  • @amoeba There's no harm doing both. Asking on meta is probably a good idea, especially since more people can have input (actually, there's no convenient way for even the mods to discuss a flag - we can't attach comments to a flag with our thoughts on what should be done, for example). – Glen_b May 17 '16 at 21:45

1 Answers1

10

A hyperparameter is a parameter for the (prior) distribution of some parameter.

So for a simple example, let's say we state that the variance parameter $\tau^2$ in some problem has a uniform prior on $(0,\theta)$.

(I personally would be unlikely to do such a thing, but it happens; I might in some very particular circumstance)

Then $\tau^2$ is a parameter (in the distribution of the data) and $\theta$ is a hyperparameter.

If we then in turn specify a (prior) distribution for $\theta$ (e.g. that it's Gamma with mean 100 and shape parameter 2), that's a hyperprior - a prior distribution on a parameter of a prior distribution.

Glen_b
  • 282,281