What does it look like to rotate and then renormalize?
There seem to be two answers. The first answer is that the highest probability event is the one farthest to the right. This event must be the entire Ω. All we do to renormalize is scale until this event is probability 1.
If we rotate until some probabilities are negative, and then renormalize in this way, the negative probabilities stay negative, but rescale.
The second way to renormalize is to choose a separating line, and use its normal vector as probability. This keeps probability positive. Then we find the highest probability event as before, and call this probability 1.
Trying to picture this, an obvious question is: can the highest probability event change when we rotate?
What does it look like to rotate and then renormalize?
There seem to be two answers. The first answer is that the highest probability event is the one farthest to the right. This event must be the entire Ω. All we do to renormalize is scale until this event is probability 1.
If we rotate until some probabilities are negative, and then renormalize in this way, the negative probabilities stay negative, but rescale.
The second way to renormalize is to choose a separating line, and use its normal vector as probability. This keeps probability positive. Then we find the highest probability event as before, and call this probability 1.
Trying to picture this, an obvious question is: can the highest probability event change when we rotate?