# Bayes

Version 1.4.0.0 (3.94 KB) by
Bayes' theorem: the discrete case.
Updated 4 Sep 2009

This m-file deals with the Bayes' theorem, as well as with the option of the frequency visualization of a given sample.

Rev. Thomas Bayes (1702-1761), developed a very interesting theorem alter known as Bayes' theorem. The work entitled 'An essay towards solving a Problem in the doctrine of Chances' was published in Philosophical Transactions of the Royal Society of London in 1764 (53: 370-418). It was not by Bayes, but it was communicated posthumously by his friend Richard Price in a letter to John Canton in december 23, 1763.

http://canoe.ens.fr/~ebrian/s1h-dhsrb/1764-bayes.pdf
Also an excellent transcription of it from:
http://www.stat.ucla.edu/history/essay.pdf

Bayes' theorem is a solution to a problem of 'inverse probability'. It gives you the actual probability of an event given the measured test probabilities. For example, you can:

-Correct for measurement errors. If you know the real probabilities and the chance of a false positive and false negative, you can correct for measurement errors.

-Relate the actual probability to the measured test probability. Bayes’ theorem lets you relate p(X|Y), the chance that an event X happened given the indicator Y, and p(Y|X), the chance the indicator Y happened given that event X occurred.

The Bayes' equation is:

p(Y|X)p(X)
p(X|Y) = -----------------------------------
p(Y|X)p(X) + p(Y|~X)p(~X)

Here, the sign ~ means complement.

Note.- According to Eliezer S. Yudkowsky's web page [http://yudkowsky.net/rational/bayes], one thing that's confusing is about the '|' notation. Reading from left to right, '|' means 'given'; reading from right to left, '|' means 'implies' or 'leads to'. Thus, moving your eyes from left to right, X|Y reads 'X given Y' or 'the probability that an element is X, given that the element is Y'. Moving your eyes from right to left, X|Y reads 'Y implies X or 'the probability that an element containing Y is X'.

Syntax: function x = Bayes(a,b,c,d)

Inputs:
a - a priori probability (prior, marginal or actual)
b - First conditional probability, p(Y|X) [option=1]; first interaction probability, p(XY) (true positive) [opion=2] or conditional probability, p(Y|X) [option=3]
c - Second conditional probability, p(Y|~X) [option=1]; second interaction probability, p(X~Y) (false positive) [opion=2] or interecation probability, p(~XY) [option=3]
d - Option = 1(default),2,or 3
- It shows a dialog whether or not you are interested with the frequency visualization of a given sample

Output:
x - chance positive test or positive result (posterior probability)
- frequency visualization of a given sample (optional)

### Cite As

Antonio Trujillo-Ortiz (2024). Bayes (https://www.mathworks.com/matlabcentral/fileexchange/25203-bayes), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R14
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Categories
Find more on Image Filtering and Enhancement in Help Center and MATLAB Answers

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
1.4.0.0

Text was improved.

1.3.0.0

Text was improved.

1.1.0.0

It was added an appropriate format to cite this file.

1.0.0.0