In Bayesian analysis, a prior distribution assigns probabilities to the possible values of an unknown parameter
before the current data are taken into account. If its density is 
and the observed data have likelihood
function 
,
then Bayes' theorem gives the posterior
distribution with density proportional to 
. A prior distribution may encode previous
information or may be chosen to have a comparatively small influence on the posterior.
Prior Distribution
See also
Bayes' Theorem, Bayesian Analysis, Likelihood Function, Posterior DistributionExplore with Wolfram|Alpha
References
Berger, J. O. Statistical Decision Theory and Bayesian Analysis, 2nd ed. New York: Springer-Verlag, 1985.Cite this as:
Weisstein, Eric W. "Prior Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PriorDistribution.html