Question

I have a piece of data that is 'parametric'. Does this mean that I can parse through the entire data just by shifting around a given set of parameters? In other words, all I have to do is change the values of a fixed set of parameters, and I can generate the original dataset?

Answer 1

No, parametric means that the whole data set "depends" (in a probability sense) on a certain number of fixed parameters. More precisely, the probability distribution from which the data is extracted depends uniquely on a fixed number of parameters. For instance, if I had given you a data set and told you they were Normally distributed, you would know that their sample mean value and sample variance would be fixed. And so would be for the future observations.