There are special cases like disease modeling (though even there predictions can be wildly off), but in general I think the exponential fit is almost always better than a sigmoid/function that doesn’t grow without bound unless you have strong reason to believe you’ve identified both the dampening term and the upper bound.
I find these arguments about fit strange, like they are failing to remember what we’re trying to do with predictions.
We want to have an accurate model of the future. That exponentials fit data better is nice, and maybe they are easier to predict the next point under many circumstances, but they are leaving something out.
Like suppose I’m trying to predict if I’ll be alive tomorrow. I could have a naive model that predicts I will be because I was alive every previous day. But this model is wrong in a very important way: one day I will die! That the model fails to account for this fact makes the model less useful, because even if it’s right for a long time, eventually it won’t be, and it’s a failure of the model that I’d get surprised to be dead.
I find these arguments about fit strange, like they are failing to remember what we’re trying to do with predictions.
We want to have an accurate model of the future. That exponentials fit data better is nice, and maybe they are easier to predict the next point under many circumstances, but they are leaving something out.
Like suppose I’m trying to predict if I’ll be alive tomorrow. I could have a naive model that predicts I will be because I was alive every previous day. But this model is wrong in a very important way: one day I will die! That the model fails to account for this fact makes the model less useful, because even if it’s right for a long time, eventually it won’t be, and it’s a failure of the model that I’d get surprised to be dead.