Is bounds of parameter hyperparameter? Suppose I set [Smin, Smax] to be the limits of slope of a regression, are they hyperparameter? If not, what are they called?
 A: Hyperparameters are much more broadly defined than @Ben's post would suggest.  He's not incorrect, but I would say Smax and Smin are hyperparameters.  I was taught anything you have to set for your model to work that doesn't involve the data itself is a hyperparameter that can be set to achieve different model performance.  
A: Hyperparameters occur in hierarchical Bayesian models; they are parameters that occur in the prior distribution for the initial parameters that occur in the sampling distribution.
If you are undertaking a Bayesian regression model then you have a choice of how you want to impose limits on the slope parameters in the regression.  If you are comfortable imposing fixed bounds on the slope parameters then you could treat $S_{\text{max}}$ and $S_{\text{min}}$ as fixed values that are specified by you, in which case they would be constants.  Alternatively, you could take them as unknown, in which case they would be hyperparameters with a specified prior distribution.  So the short answer is: they are hyperparameters if you choose to treat them as unknown.
