So if someone rolls a 10^6-sided die and tells you they’re 99.9% sure the number was 749,763, you would only assign it a posterior probability of 10^-3?
So if someone rolls a 10^6-sided die and tells you they’re 99.9% sure the number was 749,763, you would only assign it a posterior probability of 10^-3?
I see. I used a wrong state space to model this. The answer above is right if I expect a statement of the form “I’m 99.9% sure that N was/wasn’t the number”, and have no knowledge about how N is related to the number on the die. Such statements would be correct 99.9% of the time, and I would only expect to hear positive statements 0.1% of the time, 99.9% of them incorrect.
The correct model is to expect a statement of the form “I’m 99.9% sure that N was the number”, with no option for negative, only with options for N. For such statements to be correct 99.9% of the time, N needs to be the right answer 99.9% of the time, as expected.
So if someone rolls a 10^6-sided die and tells you they’re 99.9% sure the number was 749,763, you would only assign it a posterior probability of 10^-3?
I see. I used a wrong state space to model this. The answer above is right if I expect a statement of the form “I’m 99.9% sure that N was/wasn’t the number”, and have no knowledge about how N is related to the number on the die. Such statements would be correct 99.9% of the time, and I would only expect to hear positive statements 0.1% of the time, 99.9% of them incorrect.
The correct model is to expect a statement of the form “I’m 99.9% sure that N was the number”, with no option for negative, only with options for N. For such statements to be correct 99.9% of the time, N needs to be the right answer 99.9% of the time, as expected.