Bayes Theorem Explained

Key Takeaways

Bayes theorem is arguably one of the most critical concepts in probability. It is critical [music] for machine learning algorithms such as naive Bayes. In this example, we are going to study the relationship between homicidal behavior and video games. [music] Bayes theorem can be thought of as flipping a conditional probability. >> [music] >> We have the probability of B given A, but what we're interested in is the probability of A given B. To do this flip, we will also need the probability of A >> [music] >> and the probability of B. We plug those three pieces of information together, and that will give us probability A given B. Let's say there was a study >> [music] >> that found that the probability of being a gamer given someone is homicidal is .85. So, that is not the same as the probability of being homicidal given you're a gamer. To reverse the direction of this probability, we will need a [music] few more pieces of information. Approximately .19 plays violent video games in the United [music] States. According to the FBI, about .01% of the population is homicidal. [music] We plug in those three values into Bayes theorem in the formulation, and we will find that this evaluates to .0004. >> [music] >> So, a .04% likelihood that you are homicidal given you're a gamer. So, this is actually a very small number and very different than the 85% claim we talked about earlier.