Bayes' Theorem

I decided to write an article about Bayes' theorem as it is a recurrent topic in artificial intelligence and its understanding can be quite useful in everyday life (especially if you like gambling). The best example to introduce Bayes' theorem is the Monty Hall problem. Let's play a game! Considering that we have 3 doors with one of them hiding a reward, you must first pick one of the doors without opening it, so you do not know its content. Then, following the script, one of the two doors that haven’t been selected will be opened and will not hide the reward. Now, the real problem starts, would you exchange the door that you have selected for the other door, or would you keep it ?

Most people will tend to say that it does not change anything but it is actually more interesting to pick the last door. You’re skeptical ? So was I when I first learnt about Bayes theorems but it has shown to work very well. The fact that people do not easily understand Bayes theory is simply because the human brain is not optimised for rational decisions.

Bayes theory supports the idea of Bayesian networks, which are statistical models permitting to estimate the possibility of occurrence of events depending of previous events. Even though some agencies use those models to attempt guessing places of the next acts of terrorism, we are more interested in the attempt to predict different behaviors. For instance, Bayesian networks are used to predict the future driving behavior of a person, only by knowing the previous behavior/accidents, which could be useful for car insurance companies [1]. However, we might wonder how reliable such systems are, considering that human beings do not think and behave rationally. Nevertheless, we can assume that such networks are as reliable as any computational model. Those systems all suffer from the same weakness which is that they are all deterministic, which does not seem to be true for the human brain.  

But why are we not rational ? What purpose does it serve to be that influenced by emotions in our decision-making process ? It is true that not being totally rational in our decision making process may be quite handy for creativity and therefore, to evolve. It would have been quite difficult for the human race to innovate if humans all behaved and reacted in the same way.

The movie "21" explains briefly the Monty Hall Problem :

[1] Kumagai, Toru, and Motoyuki Akamatsu. "Prediction of human driving behavior using dynamic bayesian networks." IEICE TRANSACTIONS on Information and Systems 89.2 (2006): 857-860.