Multistate, Multinomial

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Also see:  M-state

KL-distance from p1 to p2

E.g. Consider these two distributions over {A, C, G, T}:
  A C G T  
p1 1/4 1/4 1/4 1/4 pr
2 2 2 2 -log pr, bits
p2 1/2 1/4 1/8 1/8 pr
1 2 3 3 -log pr, bits
               1    1    1    1    1
KL(p1, p2) = - -1 + -0 + -1 + -1 = - bits
               4    4    4    4    4
               1    1    1    1    1
KL(p2, p1) =   -1 + -0 - -1 - -1 = - bits
               2    4    8    8    4
So KL(p1, p2) = KL(p2, p1) in this case -- but not in general.
 
 
Now you calculate the two distances for these two distributions:
  ACGT
p1 1/21/41/81/8
p2 1/81/21/41/8
KL(p1, p2) = ...
KL(p2, p1) = ...
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