X-Message-Number: 19949
Date: Fri, 30 Aug 2002 09:07:46 EDT
Subject: probability estimates again

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Thomas Donaldson asked again how you find a valid estimate of probability. 
I'll try to make it a little clearer.

A probability is the relative frequency of occurrence of an event in a 
recorded sequence of experiments or observations. The sequence can be long or 
short; it is always finite. The events in the sequence can be 
indistinguishable to the observer or only similar. The longer the sequence, 
and the more nearly indistiguishable the events, the more accurate the 
probability estimate. (Very little work has been done on second order 
probabilities, the probability and variance of a probability etc.)

If a Martian were to arrive and immediately bet on a football game, he could 
only flip a coin or choose a team by an arbitrary criterion, since he has no 
useful information--"equal ignorance." But it is within his ability to 
improve his choice by learning a little about the game--maybe read about the 
AP writers' poll, which has a record of (say) 75% predictive success. At that 
point, he will favor the AP chosen team by the indicated amount. If he 
pursues his studies he can learn more and get more useful odds. But ANY 
history-based information is better than none. In the Martian's case, even 
the coin-flipping serves a purpose--it prevents him from giving or taking 
long odds.

Basically, we are talking about  experimental design. Many scientists are 
poor at it, and it can't be easily taught--but by their fruits shall ye know 

Robert Ettinger


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