Comparison of Bayesian and Classical Analysis for a Class of Decision Problems
ARMY MATERIEL SYSTEMS ANALYSIS ACTIVITYABERDEEN PROVING GROUND MD
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The report is concerned with decision making under uncertainty for the class of problems where the uncertain parameter is the Bernoulli success probability, p. For decision making purposes the desired information is frequently the probability of meeting a specific requirement for p. This problem is analyzed from both the classical and Bayesian points of view. The use of the posterior beta distribution obtained from the Bayesian updating procedure is discussed for this class of decision problems. A method for constructing a prior distribution, and a detailed example of the updating procedure with emphasis on this method, are also presented. A comparison is made of the Bayesian and the most popular classical point and interval estimation techniques. These techniques are not directly applicable in evaluating the chances of meeting a specific requirement for p. However, for certain non-trivial estimation problems, where a point of interval estimate is sufficient, the Bayesian procedure deserves consideration.
- Statistics and Probability