ABSTRACT
For a frequentist statistician, prediction means guessing the value of an unobserved random variable (rv) of interest, while estimation corresponds to guessing the value of an unknown, but fixed, parameter. Thus, the former is conceptually different from the latter, and hence different, though similar, optimality criteria have to be developed to determine best predictors and prediction regions. These subtle differences between the problem of estimation and of prediction in a general linear model context are highlighted in Bibby and Toutenberg (1977). In contrast, for a Bayesian, both are essentially the same. In any case, prediction procedures form an important component of inferential procedures associated with the exponential distribution. Geisser (1986) points to the long history of prediction problems by noting that Bayes had considered such a problem in 1763. In this chapter, we describe several scenarios where prediction is the problem of interest, discuss various predictors proposed in the literature, and study their properties. We will present a survey of the area and hopefully cover all major contributions in our effort to do so.
