In statistical inference, the frequentist perspective considers the parameter θ to be a fixed, but unknown quantity. Statistics used for inferential purposes ideally have specific optimal properties (like sufficiency). In Bayesian inference, these same properties are still desirable. However, Bayesian inferential methods also include modeling the uncertainty in our belief about θ via a prior distribution π(θ). Information in the form of a random sample x is collected from the population indexed by θ. The posterior distribution of θ given x is found using Bayes's theorem. The loss function determines the exact form of the Bayes estimator via Two Bayes Rules.