﻿ Bayes’ theorem: What is it, Examples, Formula, History, FAQ

# Bayes’ Theorem

## Bayes’ theorem

The Bayes Theorem is a sophisticated mathematical formula that dates back to the 18th century. It is frequently used in finance to calculate or update risk evaluation. Corporate financial experts have used Bayes theorem in financial and commercial circles for decades.

## What is Bayes’ theorem?

Bayes’ theorem is a statistical formula that can be used to calculate the probability of an event occurring, given the prior probability of the event and the likelihood of the event. This theorem can also be applied to financial decision-making in several ways.

For example, Bayes’ theorem can calculate the probability of a stock price moving up or down, given the stock’s past performance. You can use this information to make investment decisions.

Additionally, Bayes’ theorem can be used to calculate the probability of a company defaulting on a loan, given the company’s financial history. This information can help you assess the risk of investing in the company.

## Understanding Bayes’ theorem

According to Bayes’ theorem, events are tests that show the likelihood of something happening. Although tests aren’t events and testing outcomes are almost always inaccurate, Bayes regarded tests as a technique to gauge the likelihood that an event would occur.

Changes in interest rates can significantly impact the value of specific assets. So, the value of specific profitability and efficiency ratios used to represent a company’s performance can be significantly impacted by changes in asset value.

Companies may assess systematic changes in interest rates more accurately and direct their financial resources to gain the most benefit by using the Bayes Theorem and estimated probability.

Financial decision-makers have a stronger base for directing resources and making crucial decisions by including probability predictions in the net income calculations.

Financial institutions may also make better judgments and assess the risk of providing money to new or existing borrowers using the Bayes Theorem conditional probability model.

For instance, a current customer may have a solid history of repaying debts, but recently the customer has been slow to play. As per probability theory and additional facts, the lender may raise interest rates or reject the loan entirely if the borrower has a history of making late payments.

## Formula for Bayes’ theorem

The formula represents Bayes’ theorem: P (AB) is equal to [P(BA) P(A)] / P (B)

Where,

The probability that event A will occur following event B is expressed as P(A|B).

The probability that event B will occur after event A is expressed as P(B|A).

The probability that event A will occur is P(A).

The probability that event B will occur is P(B).

## Examples of Bayes’ theorem

For example, to understand Bayes’ theorem better, consider a drug test that is 98% accurate. In this case, the test would display a true positive result for drug users 98% of the time and a true negative result for non-users of the substance 98% of the time.

Secondly, let’s assume 5% of people use the substance. If a randomly chosen subject tests positive for the substance, the likelihood that the subject uses the substance can be calculated using the formula below.

(0.98 x 0.005) / [(0.98 x 0.005) + ((1 – 0.98) x (1 – 0.005))] = 0.0049 / (0.0049 + 0.0199) = 19.76%

In this case, even if a person tested positive, there is an approximately 80% likelihood that they did not use the drug, according to Bayes’ Theorem.

## History of Bayes’ theorem

The English mathematician and Presbyterian pastor, Thomas Bayes’ writings of “an essay towards addressing a difficulty in the theory of chances” contained Bayes’ theorem, later found and published posthumously by being read to the Royal Society in 1763.

During World War II, the theory was employed to decode the notorious German Enigma code. Using Bayes ‘ theorem, British mathematician Alan Turing evaluated the translations extracted from the Enigma-encrypted device that broke the Nazi message code.

Turing and his team finally cracked the Nazi Enigma code by using probability models to narrow down the unlimited number of potential translations depending on the message they believed most likely to be translatable.

Due to improved computing power for conducting complex calculations, Bayes’ theorem has recently gained more popularity after being long disregarded in favour of Boolean calculations.

Applications utilising Bayes’ theorem have increased as a result of these developments. These days, it is used in a wide range of probability calculations, including those involving finances, genetics, drug usage, and illness prevention.

Bayes’ theorem states that the likelihood of the second event given the first event multiplied by the probability of the first event equals the conditional probability of an event depending on the occurrence of another event.

Based on past occurrences or patterns, the Bayes law makes predictions about the future. The Bayes rule, for instance, is used in financial modelling to identify investment hazards. This theorem is also used to determine reverse probabilities by applying the conditional probability of an event.

Based on the values of individual associated known probabilities, Bayes’ theorem calculates the conditional probability of an event.

A free online tool called the Bayes’ theorem calculator shows the conditional probability of an event.

With fresh or more evidence, Bayes’ theorem offers a method for revising current predictions or theories. Bayes’ theorem is used in finance to assess the risk of loaning money to potential borrowers.

As it offers a framework for thinking about probability and making defensible uncertain decisions, Bayes’ theorem is considered an essential and significant topic in various domains.

The Bayes’ Theorem’s formula is P(A|B) = P(B/A)P(A) / P. (B). The probability of event B occurring given event A multiplied by the likelihood of event A occurring by itself makes up your numerator. After that, you divide this by the numerator of the likelihood that event B will occur on its own.

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