Statistical decision theory (Q368379)

This text is an introduction to the decisional approach to statistical inference. The author does not conceal an apologetic purpose. No complete covering of the subject is intended, and the book focuses on the main concepts and some illustrative problems. The Bayesian paradigm is favoured, although the classical (frequentist) perspective is also considered. The style is terse, but the scheme theorem/proof is not followed. Although the standard classical statistical inference approach is summarized, it is unlikely that a reader without a sufficient previous knowledge of this standard approach can take full advantage of the book. An adequate background of linear algebra, calculus and elementary probability theory (including the main distributions) is also required. The general framework is that of aid to decisions. The analyst faces a client without appreciable statistical knowledge. The basic product offered by the analyst (and the book) is a schedule with a conclusion for every prior distribution and loss function (within the families considered). In a further stage the analyst has to elicit from the client a set of plausible priors and a set of plausible loss functions (these sets can be refined iteratively). At the end of the process, either a final decision is drawn, or an impasse is declared.