Comment by analog31
3 days ago
That brings up an interesting issue, which is that many systems do have more noise in y than in x. For instance, time series data from an analog-to-digital converter, where time is based on a crystal oscillator.
3 days ago
That brings up an interesting issue, which is that many systems do have more noise in y than in x. For instance, time series data from an analog-to-digital converter, where time is based on a crystal oscillator.
Well yeah, x is specifically the thing you control, y is the thing you don't. For all but the most trivial systems, y will be influenced by something besides x which will be a source of noise no matter how accurately you measure. Noise in x is purely due to setup error. If your x noise was greater than your y noise, you generally wouldn't bother taking the measurement in the first place.
“ If your x noise was greater than your y noise, you generally wouldn't bother taking the measurement in the first place.”
Why not? You could still do inference in this case.
You could, and maybe sometimes you would, but generally you won't. If at all possible, it makes a lot more sense to improve your setup to reduce the x noise, either with a better setup or changing your x to be something you can better control.
This fact underlies a lot of causal inference.
I’m not an SME here and would love to hear more about this.