Thanks! Some very quick points: 1. I think that discontinuities like that are rare, and I’d question this one. Basically, I think that you can get ~90% of the benefit here with just a linear or exponential model, with the right uncertainty. 2. When writing a function that expresses 100 things (effectively), but in 3x the time, you wouldn’t be expected to forecast those things as well as if you spend 100x the time. In other words, I’d expect that algo forecasters would begin with a lot of shortcuts and approximations. Their worse forecasts can still be calibrated, just not as high-resolution as we’d expect from point forecasts with a similar amount of effort. I think a lot of people get caught up here, by thinking, “I have this specific model in my head, and unless I can model every part of it, the entire thing is useless”, but this really isn’t the case! 3. I fed a modified version of your question straight to our GPT-Squiggle tool, and it came up with this, (basically) no modification needed. Not perfect, but not terrible!
Thanks! Some very quick points:
1. I think that discontinuities like that are rare, and I’d question this one. Basically, I think that you can get ~90% of the benefit here with just a linear or exponential model, with the right uncertainty.
2. When writing a function that expresses 100 things (effectively), but in 3x the time, you wouldn’t be expected to forecast those things as well as if you spend 100x the time. In other words, I’d expect that algo forecasters would begin with a lot of shortcuts and approximations. Their worse forecasts can still be calibrated, just not as high-resolution as we’d expect from point forecasts with a similar amount of effort. I think a lot of people get caught up here, by thinking, “I have this specific model in my head, and unless I can model every part of it, the entire thing is useless”, but this really isn’t the case!
3. I fed a modified version of your question straight to our GPT-Squiggle tool, and it came up with this, (basically) no modification needed. Not perfect, but not terrible!
https://chatgpt.com/share/e0a65eda-77f3-45bb-bd55-d7dfec707c6f
Squiggle Link