Prior Probability

Synonyms

Prior

Definition

In Bayesian inference, a prior probability of a value x of a random variable X, P(X = x), is the probability of X assuming the value x in the absence of (or before obtaining) any additional information. It contrasts with the posterior probability, P(X = x  |  Y = y), the probability of X assuming the value x in the context of Y = y.

For example, it may be that the prevalence of a particular form of cancer, exoma, in the population is 0.1%, so the prior probability of exoma, P(exoma = true), is 0.001. However, assume 50% of people who have skin discolorations of greater than 1 cm width (sd > 1cm) have exoma. It follows that the posterior probability of exoma given sd > 1cm, P(exoma = true | sd > 1cm = true), is 0.500.

Cross References

Bayesian Methods