Prior probability
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A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. The posterior probability is then the conditional probability of the variable taking the evidence into account. The posterior probability is computed from the prior and the likelihood function via Bayes' theorem.

As prior and posterior are not terms used in frequentist analyses, this article uses the vocabulary of Bayesian probability.

Throughout this article, for the sake of brevity the term variable encompasses observable variables, latent (unobserved) variables, parameters, and hypotheses.

Informative priors

An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at noon tomorrow. A reasonable approach is to make the prior a normal distribution with expected value equal to today's noontime temperature, with variance equal to the day-to-day variance of atmospheric temperature.

This example has a property in common with many priors, namely, that the posterior from one problem (today's temperature) becomes the prior for another problem (tomorrow's temperature). The terms "prior" and "posterior" are generally relative to a specific datum or observation.

Uninformative priors

An uninformative prior expresses vague or general information about a variable. The term "uninformative prior" is a misnomer; such a prior might be called a not very informative prior. Uninformative priors can express information such as "the variable is positive" or "the variable is less than some limit".

The use of an uninformative prior typically yields results which are not too different from conventional statistical analysis, as the likelihood function often yields more information than the uninformative prior.

References

• Andrew Gelman, John B. Carlin, Hal S. Stern, and Donald B. Rubin. Bayesian Data Analysis, 2nd edition. CRC Press, 2003.

The original article can be found at: http://en.wikipedia.org/wiki/Prior_probability.
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