- published: 08 Apr 2013
- views: 21408
In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is Maximum a posteriori estimation.
Suppose an unknown parameter θ is known to have a prior distribution Failed to parse (Missing texvc executable; please see math/README to configure.): \pi . Let Failed to parse (Missing texvc executable; please see math/README to configure.): \delta = \delta(x)
, where the expectation is taken over the probability distribution of Failed to parse (Missing texvc executable; please see math/README to configure.): \theta
. An estimator Failed to parse (Missing texvc executable; please see math/README to configure.): \delta
If the prior is improper then an estimator which minimizes the posterior expected loss for each x is called a generalized Bayes estimator.