I like the distinction between target-only forecasting and reference class forecasting.
It’s interesting you use the mathematical terms zeroth and first order (and higher order) approximations, when one could take reference class forecasting into statistical terms instead: 1. Identify a reference class (relevant population from which the target was drawn) 2. Model it and make predictions
The zeroth order approximation is Yi=b0. Intercept-only model, your prediction is the average from the reference class. The first order approximation is Yi=b0+b1*X. Now there’s a slope, your prediction reflects the fact that a characteristic of the observations in the reference class varies and you can improve your prediction from that. Higher order approximations...maybe such a simple model isn’t the way to go (log-transformation? other predictors? interactions? non-linear sigmoid?).
The imperative is to try to understand the mechanism(s) that generate the reference class from which your target will be/is drawn (model it!) to make good predictions about that target.
I like the distinction between target-only forecasting and reference class forecasting.
It’s interesting you use the mathematical terms zeroth and first order (and higher order) approximations, when one could take reference class forecasting into statistical terms instead:
1. Identify a reference class (relevant population from which the target was drawn)
2. Model it and make predictions
The zeroth order approximation is Yi=b0. Intercept-only model, your prediction is the average from the reference class.
The first order approximation is Yi=b0+b1*X. Now there’s a slope, your prediction reflects the fact that a characteristic of the observations in the reference class varies and you can improve your prediction from that.
Higher order approximations...maybe such a simple model isn’t the way to go (log-transformation? other predictors? interactions? non-linear sigmoid?).
The imperative is to try to understand the mechanism(s) that generate the reference class from which your target will be/is drawn (model it!) to make good predictions about that target.