```X-Message-Number: 19949
From:  var s1 = "Ettinger"; var s2 = "aol.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>");
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
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
them.

Robert Ettinger

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