What is Bayes’ Theorem?
The Bayes Theorem, named after the 18th-century British mathematician Thomas Bayes, is a mathematical formula for calculating conditional probability. The likelihood of an outcome occurring based on a previous result occurring in similar circumstances is conditional probability. Given new or additional evidence, Bayes’ theorem allows you to revise existing predictions or theories (update probabilities).
Bayes’ Theorem can be used in finance to assess the risk of lending money to potential borrowers. The theorem, also known as Bayes’ Rule or Bayes’ Law, is the cornerstone of the field of Bayesian statistics. Click here to learn about ITR 2.
Understanding Bayes’ Theorem
Bayes’ Theorem has many applications that are not limited to finance. For example, Bayes’ theorem can be used to determine the accuracy of medical test results by taking into account how likely any given person is to have a disease and the test’s overall accuracy. To generate posterior probabilities, Bayes’ theorem incorporates prior probability distributions.
In Bayesian statistical inference, prior probability is the probability of an event occurring before new data is collected. In other words, it represents the best rational assessment of the probability of a specific outcome based on current knowledge before the execution of an experiment.
The revised probability of an event occurring after taking into account new information is known as posterior probability. Using Bayes’ theorem, the posterior probability is calculated by updating the prior probability. In statistics, the posterior probability is the likelihood of event A occurring, given that event, B has already occurred.
Bayes’ Thus, the theorem provides the probability of an event based on new information that is or may be related to that event. The formula can also determine how hypothetical further details may affect the probability of an event occurring, assuming the new data is accurate.
Consider drawing a single card from a complete deck of 52 cards.
The probability of the card being a king is four divided by 52, which equals 1/13. Keep in mind that the deck contains four kings. Assume the selected card is a face card. Given that the chosen card is a face card, the probability is four divided by 12, or approximately 33.3 per cent, as there are 12 face cards in a deck.
The theorem was discovered in the papers of English Presbyterian minister and mathematician Thomas Bayes and was published posthumously in 1763 by being read to the Royal Society. Bayes’ Theorem, which was long ignored in favour of Boolean calculations, has recently gained popularity due to increased calculation capacity for performing its complex calculations.
These advancements have increased the number of applications that use Bayes’ theorem. It is now used in a wide range of probability calculations, such as financial calculations, genetics, drug use, and disease control.
In its most basic form, Bayes’ Theorem takes a test result and relates it to the conditional probability of that test result given other related events. The Theorem provides a more reasoned likelihood of a particular outcome for a high probability of false positives. Check this to learn about the functions of insurance.