prior probability distribution

In statistics, a prior probability distribution represents the initial beliefs about a population parameter before any new evidence is considered. This distribution is a crucial component of Bayesian analysis, a statistical inference method developed by Thomas Bayes.12

Bayesian analysis combines this prior information with evidence from a sample, using Bayes's theorem to produce a posterior probability distribution. This updated distribution reflects the refined understanding of the parameter after incorporating the new data. A key aspect, and a point of discussion among statisticians, is that Bayesian methods allow for probability distributions to be assigned to unknown parameters, which contrasts with classical statistics where parameters are treated as fixed constants. This approach can incorporate both objective data and subjective opinions to define the prior distribution.12