From: Hal Finney <hal@rain.org>

Date: Sun Apr 26 1998 - 19:45:03 PDT

Date: Sun Apr 26 1998 - 19:45:03 PDT

Robin Hanson writes:

*> If you find your estimate to be very senstive
*

*> conditioning on each new peice of information you consider when trying
*

*> to construct your estimate, you might want to guess at a distribution
*

*> over what your estimate will be if your thought about it for another
*

*> ten minutes. That is a legit probability over probabilities.
*

Yes, I can see that there would be situations where your internal

probability estimate is converging too slowly to come up with a meaningful

final figure.

My wife suggested another case, where experimental results are being

expressed in probabilistic terms (like, the probability of a 50 year

old woman dying of breast cancer is X%, and increases to Y% if her

mother had the disease). In that case there may be error bars from the

underlying statistics which were used to derive the probabilities.

*> Note that none of this requires any revision of the standard
*

*> probability picture.
*

In the standard mathematical theory of probability, probability is defined

as a measure function over a set of disjoint outcomes, such that the sum

of the measures of all the outcomes is 1. Can the idea of "probability

of probability" be formalized? Do all probabilities have a probability?

My son (age 15) suggested that a probability of 100% should always itself

have a probability of 100%. It would not make sense, he thought, to say

that there was a 90% probability that the probability of an event is 100%.

Either an event is certain or it is not, and you should not say that it

is certain unless you are certain that it is certain. Does that make

sense?

I am still not completely comfortable with these second order

probabilities. It makes me wonder why we stop there.

Hal

Received on Mon Apr 27 02:45:48 1998

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