06/11/2019

The Bayesian perspective on artificial intelligence

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

I've written about probability before , but I've never discussed the most basic question: what is the probability of an event and how can it be determined? In many cases, there is a straightforward answer. For example, when we flip a coin many times, it lands on heads about half the time. So, the probability of the event "heads" is 50%.

But this approach, called frequentist, is not always adequate. What is the probability of Brazil winning the 2022 World Cup? We cannot repeat the competition to count how many times Brazil has won. For such situations, there is the Bayesian perspective.

The name honors the English Reverend Thomas Bayes (1701-1761), a pioneer in the use of probability in problem-solving. But Bayesian probability as we understand it today is primarily due to the Frenchman Pierre-Simon de Laplace (1749-1827), who rediscovered Bayes' ideas and disseminated them.

For Bayesian mathematicians , the probability of an event is the expectation that it will occur, based on available information. It is therefore subjective, since it depends on the information accessible to each person. This is quite surprising for a mathematical theory!

Bayes presented a formula to improve the probability estimate based on each new piece of information. I will illustrate with the following question: when an HIV test is positive, what is the probability that the person is actually infected?

Let's assume the chance of error in the test—giving a positive result for a healthy person or a negative result for an infected person—is 0.2%. With such a low chance of error, we would conclude that the probability of someone testing positive being infected should be almost 100%. But let's also assume that it is known that those infected make up 0.1% of the population. Using this new information, Bayes' formula gives that the probability of someone testing positive being infected is only 33%.

To read the full text, visit the newspaper's website or check the print version .