Concept
How does Bayes’ Theorem make difficult probabilities easier to estimate?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Another trick that helps compute probabilities in practice is Bayes’ Theorem. We’ve defined Pr( A | K ) as Pr ( A ∩ K ) Pr ( K ) , and by swapping the letters we get Pr( K | A ) = Pr ( K ∩ A ) Pr ( A ) . Combining these with a little bit of algebra yields: Pr ( A | K ) = Pr ( K | A ) Pr ( A ) Pr ( K ) Now this is a very, very powerful equation that has a multitude of uses throughout computer science and statistics. What makes it powerful is that it allows us to express Pr( A | K ), a quantity often very difficult to estimate, in terms of Pr( K | A ), which is often much easier."
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