instruere...inlustrare...delectare Disputations

Wednesday, August 05, 2009

An observation

Bayes' Law is a mathematical equation that can be used to revise an estimate of the probability that some unobserved event has or will occur, based on observing some other event that is correlated in some known way with the unobserved event.

For example, a Bayesian inference engine might increase it's estimate that you have been cursed by Mme deGuerre after being told you were awakened by a strangled cry in the dead of night.

It's a well-known property of Bayes' Law that how much the estimate changes depends on what the estimate was prior to the other event being observed.

This is also true, of course, of people who aren't explicitly using Bayesian inference. Two people can observe the same event and assign it different levels of significance.

A less-mentioned property (perhaps because it's less interesting mathematically) of Bayes' Law is that the prior estimate of the probability of observing the event is also a function of the prior estimate of the probability of the unobserved event. The greater the prior probability you've been cursed by Mme. deGuerre, the more the inference engine tells you to expect to be awakened by a strangled cry in the dead of night.

Psychologically speaking, if you're expecting something, then you're more likely to observe it -- whether it really happens or not.

Thus, even if two people agree on how things that can be seen are influenced by things that can't be seen, they can still disagree on how important what they see is, and even on what they see.