ABSTRACT

In this chapter we consider interval estimation of a single parameter and region estimation of a vector of parameters. The Bayesian decision theoretic approach considers the choice of a particular interval or region for an unknown parameter as a decision-making problem. Optimal intervals are sought to minimize an expected loss. The Bayesian inferential approach does not make use of the notion of a loss function. Instead it considers the posterior distribution of an unknown parameter as an inferential statement and may set regions for the parameters under the derived posterior distribution. They may be quantitatively similar to regions obtained by a non-Bayes approach but their interpretation is clearly different.