Bayes' theorem

P(parameters given data) ~ P(data given parameters) × P(parameters)

  • P(parameters given data): is called posterior
  • P(data given parameters): is called likelihood
  • P(parameters): is called prior

Videos

Derivation of Bayes rule + Chain rule for probs

It is astonishing simple.
                                                   P(A,B)
The conditional prob P(A|B) is defined as P(A|B):= ------
                                                    P(B)
So P(A,B) = P(A|B) P(B) - if P(B)>0

And for this:

         P(B|A)P(A)
P(A|B) = ----------
            P(B)
            
<=> P(A|B)P(B) = P(B|A)P(A)
<=> P(A,B) = P(A,B)             

Simple example

Computing the probability of having found a hipster in NYC given some data (“drinking PBR”). Nice example by Student Dave.

 
public/bayes_theorem.txt · Last modified: 2014/01/01 19:11 (external edit) · []
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