What are the hyperparameters? I find the meaning of hyperparameters not always clear. The hyperparameters are defined as "the parameters of the prior". Suppose that one has prior information about a certain parameter $\theta$. More precisely, one supposes that $\theta \sim N(\mu_0, \sigma_0^2)$. In that case, the hyperparameters are given by $\mu_0$ and $\sigma_0^2$.
But, what in case of a non-informative prior? What in case of a uniform prior? For instance, suppose we have the following model. We have data $y_1,\ldots,y_n$ where the likelihood is given conditionally on a parameter $\lambda$. Thus:
$$y_i \ | \ \lambda \sim N\left(\mu,\frac{\sigma^2}{\sqrt{\lambda}}\right), \qquad \lambda \sim \Gamma(\nu/2,\nu/2)$$
with the non-informative prior $g(\mu, \sigma^2) \sim 1/\sigma$. So we have in fact three parameters $\lambda, \mu, \sigma^2$. What are the hyperparameters in this case? 
 A: In your example: 


*

*if $\nu$ is known there are no hyperparameters. A model does not require to have hyperparameters. 

*if $\nu$ is unknown and you set a prior on it, then $\nu$ would become an hyperparameter. 


Nevertheless, I do not understand why $\mu$ and $\sigma$ do not appear in you conditioning and I guess that you did that because there are what is often call a nuisance parameter (meaning that they appear in your modeling but are not of interest ($\lambda$ seems to be your parameter of interest)) which is (from a terminology perspective) different from an hyperparameter. So:


*

*$\lambda$ is your parameter of interest,

*$\mu$ and $\sigma$ are nuisance parameters.


Then from a practical perspective, in most (but not all) cases, there is to IMHO no difference between nuisance parameters and hyperparameters (in most cases, hyperparameters are "nuisance hyperparameters"), both are here to be marginalized out.
For a more broad discussion about the definition of an hyperparameter see What exactly is a hyperparameter?.
