Equal Probabilities from Shannon Entropy
Note that the probabilities are all equal to 1/n, and the Lagrange multiplier is equal to -log (n).
Monday, March 14, 2005
Equal Probability
Suppose, following Laplace's "principle of indifference", that there is a finite number, n, of exclusive possibilities. Then, if the possibilities cannot be distinguished beyond their identification, each is assigned a probability equal to 1/n. (e.g.: link). It so happens that Shannon's entropy, S, satisfies the principle of indifference:
Equal Probabilities from Shannon Entropy
Note that the probabilities are all equal to 1/n, and the Lagrange multiplier is equal to -log (n).
Equal Probabilities from Shannon Entropy
Note that the probabilities are all equal to 1/n, and the Lagrange multiplier is equal to -log (n).
