Doing this will be the main business of this article.
First, however, we provide some historical and philosophical context in order to motivate the reader for the technical work ahead.
The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern (1944).
What does it mean if a test for some disease is "95% accurate"?
Does it mean that, if you test positive, you have a 95% chance of having the disease.
While this sounds sensible, the answer is usually "no." The actual probability depends not only on the reliability of the test, but also the number of infections in the population to begin with. Go to the applet It is often difficult to observe effort on the part of employees, so companies are forced to reward employees based on success or failure (a measure of performance) which is only partially controlled by effort.
How likely is it that bonuses are going to the bad employees, who simply et lucky, rather than the good ones?
Treating probability as a logic, Thomas Bayes defined the following: Pr(A|B)=Pr(B|A)Pr(A)/Pr(B) For example, probability that the weather was bad given that our friends played soccer can be calculated as: Pr(play soccer in the rain)Pr(rain)/Pr(play soccer).
) of those agents, where the outcomes in question might have been intended by none of the agents.
The meaning of this statement will not be clear to the non-expert until each of the italicized words and phrases has been explained and featured in some examples.
Engineers see references to Bayesian Statistics everywhere.
Here is a ten-minute overview of the fundamental idea. But there's a catch: Sometimes the arithmetic can be nasty.