Bayesian theory

Definition:
A name applied generically to statistical decision theory, even where the methods employed do not depend upon the theory proposed by Thomas Bayes during the 18th century. Enis and Broome (Marketing Decisions: A Bayesian Approach, 1971) summarize the Bayesian approach as consisting of five elements, namely: (a) The decision-maker is involved in a situation in which there are at least two alternative ways of reaching a specific objective(s), and he has the power to decide among the alternatives. (b) The decision-maker is uncertain as to which decision alternative to select, because he does not know the set of environmental conditions (state of nature) which will actually prevail at the time the decision is implemented. (c) The decision-maker has some knowledge of the situation, e.g. relative pay-offs of alternatives, and the likelihood of the occurrence of various events or states of nature which affect these pay-offs. (d) The decision-maker is willing to use expected value as his decision criterion. (e) The decision-maker may be able to obtain additional information (at some cost) which might change his assessment of the situation. Thus three concepts are central to the Bayesian methodology: (i) the identification of alternatives; (ii) the assignment of probabilistic expectations to the alternatives: and (iii) the use of expected value as the decision criterion.

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