Decision Theory
The businessman has to operate in an atmosphere of uncertainty and has to select the best course out of several alternative courses of action that may be available to him. In earlier days, decisions were made mainly on personal judgement. However these days judgement is combined with several quantitative techniques and the best action is arrived at in a given situation. The test of hypothesis procedures in earlier chapter was designed to test a statistical statement about a population (the null hypothesis given a level of significance.
The hypothesis testing is sometimes called classical decision theory. In hypothesis testing, the statistical decision is to either accept or reject the null hypothesis. The classical decision procedure has the following three major defects:
First, it provides for only two possible actions which correspond to either acceptance or rejection of the null hypothesis. Also, it allows only two states of the parameter being tested, that is those parameter values that make the null hypothesis true and those values for which the null hypothesis is false. However, in most practical decision problems, a decision maker should be able to make a choice from among several different acts or subject to a wide variety of states or conditions over which he or she has no control.
Secondly classical decision procedure does not recognize the validity of information pertaining to the decision that does not exist in the form of empirical data that result from a process of sampling.
Thirdly, there are real economic consequences that result from making a wrong decision. Although such consequences might be considered by the decision-maker using the classical procedure in selecting the significance level for the test, these considerations are never an explicit part of the decision model or procedure. The Bayesian decision making procedure bases its decision upon a direct evaluation of the payoff for each alternative course of action
The statistical decision theory, also called Bayesian decision theory or simply decagons theory removes the above shortcomings and enables optimal decisions to be taken. Its main strengths are: first, it provides a model for decision-making in situations that involve multiple states of the parameter, or nature, there commonly used in decision theory. Secondly, it incorporates the economic consequences of wrong decisions directly into the decision-making model. Thirdly, it allows the use of information pertinent to the problem which exists prior to any sampling or experimentation, whether this information is in t5he form of empirical data or is subjective assessment of the decision maker.
Some of its main topics are:
1. Decision tree analysis
2. Decision problem ingredients
3. Optimal decisions
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