Posterioriestimatorer

Posterioriestimatorer is a term encountered in some educational or theoretical discussions of Bayesian decision theory to denote a class of estimators derived from the posterior distribution of a parameter. In this framing, estimators are obtained by applying a decision rule that minimizes expected loss with respect to the posterior distribution p(theta | data), combining prior information with observed evidence.

In practice, one specifies a prior p(theta) and a likelihood p(data | theta) to obtain the posterior p(theta | data). A loss function L(theta, a) is chosen to reflect the cost of declaring an estimate a when the true value is theta. The posterioriestimatorer then selects the action a_hat that minimizes the posterior expected loss: a_hat = argmin_a E[L(theta, a) | data]. Common examples include choosing the posterior mean under squared error loss and the posterior median under absolute error loss. The framework also supports uncertainty quantification through credible intervals or posterior predictive checks.

The term is not a standard technical designation in most statistics literature but rather a pedagogical label used to emphasize how different loss choices translate posterior beliefs into concrete estimates. It highlights the connection between priors, likelihoods, and decision rules, and how these elements influence point estimation and uncertainty assessment.

Applications are typically discussed in the context of Bayesian estimators, particularly when robust or decision-theoretic properties are of interest. Limitations include dependence on the prior, computational complexity for complex models, and sensitivity to the chosen loss function. See also Bayesian estimator, posterior distribution, and Bayesian decision theory.