Sure. Though I note that if you’re already communicating a regional map with thousands of locally-fit parameters, you’re already sending a file, and at that point it’s pretty much as easy to send 10MB as 10KB, these days. But there’s all sorts of other reasons why parametric models are more useful for things like rendering causal predictions, relating to other knowledge and other results, and so on. I’m not objecting to that, per se, although in some cases it provides a motive to oversimplify and draw lines through graphs that don’t look like lines...
...but I’m not sure that’s relevant to the original point. From my perspective, the key question is to what degree a statistical method assumes that the underlying generator is simple, versus not imposing much of its own assumptions about the shape of the curve.
Sure. Though I note that if you’re already communicating a regional map with thousands of locally-fit parameters, you’re already sending a file, and at that point it’s pretty much as easy to send 10MB as 10KB, these days. But there’s all sorts of other reasons why parametric models are more useful for things like rendering causal predictions, relating to other knowledge and other results, and so on. I’m not objecting to that, per se, although in some cases it provides a motive to oversimplify and draw lines through graphs that don’t look like lines...
...but I’m not sure that’s relevant to the original point. From my perspective, the key question is to what degree a statistical method assumes that the underlying generator is simple, versus not imposing much of its own assumptions about the shape of the curve.