Prior Probability

A prior probability distribution, often called simply the prior, of an uncertain quantity p  is the probability distribution that would express one's uncertainty about p before the "data" are taken into account. It is meant to attribute uncertainty rather than randomness to the uncertain quantity.

When we multiply the prior by the likelihood function and then do normalizing, we get the posterior probability distribution, which is the conditional distribution of the uncertain quantity given the data.

A prior is often the purely subjective assessment of an experienced expert. Some will choose a conjugate prior when they can, to make calculation of the posterior distribution easier. Prior probability is assessed in the absence of empirical data, or which may incorporate pre-existing data and information. The posterior probability can be calculated by Bayes' theorem from the prior probability.

In many cases the sum or integral of the prior values may not even need to be finite to get sensible answers for the posterior probabilities. When this is the case, the prior is called an improper prior. Some statisticians use improper priors as uninformative priors.