Comment by mitthrowaway2
1 hour ago
No, what I'm saying is that 0.7 is the ending point of the calculation, and there is no 80% associated with it. The 0.7 number already factors in my uncertainty in all of my knowledge about whether it will rain tomorrow. Saying that you're 80% sure of your 0.7 probability forecast throws a TypeErrorException.
yes and in my example the ending point of the calculation is 0.58.
I make an intermediate step explicit in this derivation because it is important for the understanding of the problem.
This kind of intermediate step happens a lot in forecasting competitions, where participants are asked for their forecasts and their confidence in their forecasts. I want to show here that you need to include that in your forecast (all you belief) and not keep it separated.
But again this seems like a TypeError.
If you're asking me for my forecast and my confidence in my forecast, I would say this:
Forecast: It will rain tomorrow. Confidence: 0.7
If you say "No no, I mean what is your confidence in the 0.7 number" then I have no idea what you're talking about. 0.7 is my confidence. It's not valid to attach a confidence to that number. When the next day comes, we simply find out whether it rains or does not rain, and whoever put the highest probability on the correct outcome wins.
If you're doing this with intermediate steps then I have to ask: where did the 0.7 probability come from as an intermediate step, and what is the epistemic meaning of the 0.8 attached to it? If you only felt 80% sure that you were 70% sure that it would rain tomorrow, then what is the proposition that you are 70% confident about?