The Simplest Way to Remember Bayes Rule
Here is a way to remember Bayes rule, together with its source rule that relates joint probability to conditional probability. I believe it is simpler and more intuitive than other attempts you may find.
(Find the more stable version of this article on medium)
The Simplest Way to Remember Bayes Rule
Joint Probability Rule. The number of samples with both properties A & B, is equal to the number of samples B weighted by the fraction of them that have property A.
(The joint probability rule can also be written relative to the number of samples A, which directly leads us to Bayes' rule.)
Bayes Rule. The number of samples with both properties A & B, is equal to the number of samples B weighted by the fraction of them that have property A, is equal to the number of samples A weighted by the fraction of them that have property B.
That's all!
Recovering the Common Version
领英推荐
The key to making this naturally intuitive to remember is thinking in terms of numbers of samples (instead of probabilities), properties (instead of events), fractions (instead of conditional probabilities). Of course, this is just an aid, helping memorize the general form. Nevertheless, it is not wrong, instead it is a faithful example, taken from the discrete case.
The Simplest Way to Remember Bayes' Rule, for Visual Folks
Imagine a bag of shapes. A shape can be a square, an checkmark X, or a checked square.
The number of squares with a checkmark, derived from the total number of all squares (checkmark or not), is the number of all squares, weighted by the fraction of the them which are checked. Similarly, derived from the number of all checked shapes (square or not), it is the number of all checked shapes, weighted by the fraction of them which are squares.
If numerical examples help you, in this case, 3 = 6 * 1/2. That is, we have 3 checked squares, because we have 6 squares (checked or not) out of which 1/2 are checked.
Going from this to the Bayes' rule is trivial as explained in the previous section.
Other Attempts
Solving and re-solving @Irreducible
2 年More stable version: https://medium.com/@jadnohra/the-simplest-way-to-remember-bayes-rule-727ff7c30221
Perception for Self-Driving Vehicles
2 年Since I understood the rule as explaining away events, this was counter-intuitive, but that makes it even more interesting!
?? Data applications work best in the Data Cloud ??
2 年This is great Jad. I think, and this is not an overstatement, society as a whole would be better if more people would understand how Bayes Rule works.