A note on the posterior expected loss as a measure of accuracy in Bayesian methods

摘要

For many Bayesians, the posterior risk (posterior expected loss), which is a function of the data and the prior information, is the only measure of accuracy of interest. It is shown here that the value of this measure of accuracy may increase (uncertainty increases) as more data are obtained. The value of the posterior variance, which the posterior risk when the loss function is the squared error one, may exceed the value of the initial measure of accuracy, which is the prior variance. A specific example is analyzed numerically using Fortran language.