**Prior Probability**

In Bayesian statistical inference, a **prior probability distribution**, often called simply the **prior**, of an uncertain quantity *p* (for example, suppose *p* is the proportion of voters who will vote for the politician named Smith in a future election) is the probability distribution that would express one's uncertainty about *p* before the "data" (for example, an opinion poll) is taken into account. It is meant to attribute uncertainty rather than randomness to the uncertain quantity. The unknown quantity may be a parameter or latent variable.

One applies Bayes' theorem, multiplying the prior by the likelihood function and then normalizing, to 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.

Parameters of prior distributions are called *hyperparameters,* to distinguish them from parameters of the model of the underlying data. For instance, if one is using a beta distribution to model the distribution of the parameter *p* of a Bernoulli distribution, then:

*p*is a parameter of the underlying system (Bernoulli distribution), and*α*and*β*are parameters of the prior distribution (beta distribution), hence*hyper*parameters.

Read more about Prior Probability: Informative Priors, Uninformative Priors, Improper Priors, Other Priors

### Famous quotes containing the words prior and/or probability:

“The logic of the world is *prior* to all truth and falsehood.”

—Ludwig Wittgenstein (1889–1951)

“Crushed to earth and rising again is an author’s gymnastic. Once he fails to struggle to his feet and grab his pen, he will contemplate a fact he should never permit himself to face: that in all *probability* books have been written, are being written, will be written, better than anything he has done, is doing, or will do.”

—Fannie Hurst (1889–1968)