Prior probability

Summary

A prior probability is the probability that we give to a hypothesis before we see the data. More generally, a prior distribution is the distribution that we give to an unknown quantity before we see the data. In Bayes' theorem the prior is combined with the likelihood of the data, and the result is the posterior probability.

Remarks

An informative prior uses real knowledge about the quantity. An uninformative prior tries to express little knowledge, for example a uniform distribution on the possible values. An improper prior is a "distribution" with infinite total mass, such as the uniform measure on $\mathbb{R}$. It can still give a proper posterior.

Explanations

L1 human

The prior is what you believe before the experiment. If $1\%$ of people have a disease, then the prior probability that a random person is sick is $0.01$, before any test is done.