Well, because a success can be caused by a process who has a high mean, but also by a process which has a lower mean and a higher standard deviation. So for example, if you learn that someone has beaten Magnus Carlsen, it could be someone in the top 10, like Caruana, or it could be someone like Ivanchuk, who has a reputation as an “unreliable genius” and is currently number 56, but who, when he has good days, has extremely good days.
Suppose you give initial probability to all three normals. Then you sample an event, and its value is 1. Then you update against the green distribution, and in favor of the red and black distributions. The black distribution has a higher mean, but the red one has a higher standard deviation.
Well, because a success can be caused by a process who has a high mean, but also by a process which has a lower mean and a higher standard deviation. So for example, if you learn that someone has beaten Magnus Carlsen, it could be someone in the top 10, like Caruana, or it could be someone like Ivanchuk, who has a reputation as an “unreliable genius” and is currently number 56, but who, when he has good days, has extremely good days.
Suppose you give initial probability to all three normals. Then you sample an event, and its value is 1. Then you update against the green distribution, and in favor of the red and black distributions. The black distribution has a higher mean, but the red one has a higher standard deviation.
Thanks, I understand what you mean now!