prior-distribution

Prior distribution is a probability distribution over the parameter space Θ of a statistical model. Remove the statistical model and the parameter space vanishes — the prior has no domain to be defined over. The concept ceases to operate as a distribution over parameters.

A prior distribution encodes prior beliefs about model parameters and is used to serve statistical inference — specifically Bayesian statistics. It serves the statistical enterprise by providing initial information that, combined with likelihood, yields posterior distributions for parameter estimation and uncertainty quantification.

Posterior distribution is computed via Bayes rule as proportional to likelihood times prior. Removing the prior removes the multiplicative factor; the posterior cannot be computed or operated as Bayesian update. Operational cessation.