X-Message-Number: 19949 From: Date: Fri, 30 Aug 2002 09:07:46 EDT Subject: probability estimates again --part1_86.1faa273a.2aa0c822_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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 them. Robert Ettinger --part1_86.1faa273a.2aa0c822_boundary Content-Type: text/html; charset="US-ASCII" [ AUTOMATICALLY SKIPPING HTML ENCODING! ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=19949