Bayes Rule an Introduction
May 10, 2018
Bayes Rule describes how to update the probability of an event happening as new evidence emerges or occurrence of some another event. The Bayes principle lets you learn as new evidence occurs.
For example, if you consider yourself a good Driver and happens to be in an accident, will you still consider yourself as a good Driver? The answer will depend on:
- Your driving history
- Weather conditions when the event occurred, was it Raining or Snowing
- What were the road conditions if it was icy or not.
- Did someone else hit you from the back?
- How was the visibility at the time of the accident?
- And many other factors
Based on answers above you may still be a really good Driver.
What if you were in another accident, Now you will question if you are still a great driver.
Though Thomas Bayes came up with the basic principle of modern Bayes Rule. The lot of work was done by someone else for quantifying the principle and publishing the Modern Bayes Rule. For some reason, he never published his paper in Royal Society as he never considered it worthy of publication.
After the death of Thomas Bayes, his friend Richard Price looked at the unpublished paper and came up with the mathematical formula for the same but his formula was nowhere close to the modern version of Bayes Rule.
Later, Pierre-Simon Laplace, a French mathematician used Bayes rule in Astronomy to compute the size of Jupiter and Saturn and came up with the mathematical formula which we know as a Bayes Rule today.
The Modern version of Bayes Rule looks Something like this:
P(A|B) = P(B|A) * P(A) / P(B)
- P(A|B): Conditional Probability that likelihood of event A occurring given that B is true.
- P(B|A): Conditional Probability that likelihood of event B occurring given that A is true.
- P(A) and P(B) are the probability of the events happening which are independent of each other.
Due to the rules ability to quantify the probability of occurrence of the event given some another event it finds many applications and is the basis of Artificial Intelligence algorithms like Spam Filtering, Drug Detection, Enigma Decoding Machine, Fraud Detection, Diagnostic Software and much more.
For more details, it’s worth reading The Theory that would not die.