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By the posterior probability in (2.4), the analyst expresses her belief about the unknown state of nature when the evidence is given and known. The interpretation of in (2.4) may therefore be a bit confusing because is known. Instead, we should interpret as the likelihood that the (unknown) state of nature is , when we know that we have got the evidence .

In our daily language, likelihood is often used with the same meaning as probability, even though there is a clear distinction between the two concepts in statistical usage. In statistics, likelihood is used, for example, when we estimate parameters (maximum likelihood principle) and for testing hypotheses (likelihood ratio test).