What is Bayes’ Theorem?
In the statistical context, Bayes’ Theorem refers to the mathematical formula that is used for calculating the probability of a certain event considering the prior knowledge related to the event. Also known as Bayes’ rule and Bayes’ law, this theorem gets its name from Thomas Bayes, a famous British mathematician. This mathematical formula helps people identify the conditional probability of an event. In simple terms, conditional probability refers to the chances of an event taking place based on past events. It also helps people revise existing rules and theories with new evidence.
Bayes’ Theorem Application
Bayes’ Theorem is extensively used in the banking and financial industry. Lenders, credit unions, banks, and other financial institutions use this theorem to calculate the risk involved in lending money to the borrower. Note that the application of the Bayes’ rule isn’t confined to the financial and statistical field. For instance, many medical specialists and practitioners apply Bayes’ theorem to identify the probability of the patient getting a disease based on their medical history and previous conditions.
It is mainly used to identify the accuracy of the medical test. The important component of Bayes’ theorem is the prior knowledge of the event. Based on the previous events and new evidence, the individual can calculate the posterior probabilities. So, what is the prior probability and how does it affect future events?
Prior and Posterior Probabilities
Basically, the prior probability refers to even prior to the latest evidence and data. In other words, it is defined as the current knowledge of the given event before new experiments are performed or the latest data about this event is collected. Posterior probability, on the other hand, is defined as the changes in the probability of an event based on the latest experiments, figures, and data.
With the help of Bayes’ theorem, researchers and scholars can revise their previous data after taking the outcome of the latest event into consideration. If you see it from the statistical perspective, then the posterior probability is defined as the chances of the event B taking place considering that event A has occurred. That being said, Bayes’ Theorem focuses on revising the current information according to the latest experiments and information around the given event. It also helps people identify the changes in the prior probabilities when the information is released. Let’s understand this with an example.
Suppose you draw one card from the deck of 52 cards. The chances this card will turn out to be the king is 4/52, which translates to approx 7.69 percent. Let’s say you have drawn a face card. Now, the chances this card will be a king card is 4/12. That means there is a 33.3% probability that the card will be a king card (since a deck features 12 face cards).
In addition to the statistical theories and financial industry, Bayes’ theorem has a wide range of applications. It is applied to the stock market, the medical industry, and other realms.