Loss Models, 5th Edition

13Bayesian Estimation

All of the previous discussion on estimation has assumed a frequentist approach. That is, the population distribution has been fixed but unknown, and our decisions have been concerned not only with the sample we obtained from the population, but also with the possibilities attached to other samples that might have been obtained. The Bayesian approach assumes that only the data actually observed are relevant and it is the population distribution that is variable. For parameter estimation, the following definitions describe the process and then Bayes' theorem provides the solution.

13.1 Definitions and Bayes' Theorem

Definition 13.1

The prior distribution is a probability distribution over the space of possible parameter values. It is denoted and represents our opinion concerning the relative chances that various values of are the true value of the parameter.

As before, the parameter may be scalar or vector valued. Determination of the prior distribution has always been one of the barriers to the widespread acceptance of Bayesian methods. It is almost certainly the case that your experience has provided some insights about possible parameter values before ...