Bayes’ theorem is used in statics to describe the probability of an event, using evidence has been given. It uses a mathematical formula to revise existing predictions given additional evidence. It was named after the 18th century British mathematician Thomas Bayes
This formula is used in many day-to-day situations, for example it is used by spam filters to determine whether an email is real or spam, given the words presented in the email.
Event A = Message is spam
Event B = Message contains certain words
After analysing the words in a message, a probability is calculated rather than making a certain yes or no decision as to whether it is spam or not. So, if the probability calculate has a 97% chance of being spam, the email most likely is. As the spam filter is trained with more messages, it updates the probabilities that certain words lead to spam messages.
In finance, it can be used to calculate the risk of lending money to potential borrowers which would be of important use in many transactions. It is created by using different conditional probabilities, which shows how probable an event is given that some other event occurs. It can also be useful in medical science as it can be used to show the likelihood of getting false positives in tests such as cancer screening and drug testing.
Game theory is the study of decision making where several people must make choices which can affect the interests of other people. It is also defined as the study of human conflict and cooperation within a situation which is seen to be competitive. This concept is used whenever the actions of several people are interdependent, for example in an oligopolistic market. It lays out the players (a.k.a. the agents), their preferences, their information, the strategic actions available and how these may influence the outcome. An assumption that is usually made when considering the game theory is that the players are rational, which means that they will act in their own best interest, given what he expects his competition to do.
In game theory, a Bayesian game is a game in which the players do not have complete information on the other players. For example, one player may be unaware of the other player’s available strategies. This is called the Bayesian game because probability is used when making assumptions. At the start of the game, players have assumptions about the opposite player, and can update their assumptions as they change using Bayes’ theorem as the game takes place.