Suppose, for example, that we have observed N independent flips of a coin which we regard as having a constant probabilty, p, of falling heads up. The likelihood function is then the product of N factors, each of which is either p or 1-p. If we observe X heads and N-X tails, then the likelihood function is
No multiplicative constant of C(N,X) is included because only the part of the probability which involves the parameter, p, is relevant. In particular, this principle suggests that it does not matter whether you started out planning to observe N trials or you just decided to stop on a whim. The issue of the likelihood principle is still controversial. A deeper discussion of the topic is available in the article about the maximum likelihood principle.
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