Friday, May 11, 2012

Bayes Estimators, Loss Functions, and J. M. Keynes

As a result of my recent post on Bayesian estimation of a simple consumption function, a few people emailed asking for proofs of the results that the Bayes estimator is the mean (a median) [a mode] of the posterior density, when the loss function is quadratic (absolute error) [zero-one].

Let's take a look at this, for the case of a single parameter.