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1 2010

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Should we use a uniform prior in probabilistic decision making?

Piegat A., Landowsky M.

Foundations of Computing and Decision Sciences

2010

Vol. 35, No. 1

43--61

In probabilistic decision-making and diagnostics problems solved with the use of Bayes' theorem and in Bayes' networks if a priori distribution of probability density is not known the uniform distribution is assumed to determine the working, approximate solution of the problem. However, in many practical problems experts possess some qualitative knowledge about a priori distribution, e.g. the distribution is unimodal (one maximum) or it is unimodal right-asymmetric one, etc. It was explained in the paper that in such cases we need not unconditionally use the uniform distribution but we may use other types of distributions which better correspond to our qualitative knowledge and to the reality. However, to determine a priori distribution compatible with our qualitative knowledge we have to calculate the approximate, average, limit distribution the AAL- distribution of an infinitely large number of all possible distributions that possess the given qualitative feature, e.g., which are unimodal and right-asymmetrical ones. Is it possible at all? In the paper it was shown that it is possible if a special method conceived by one of the authors, the method of event-granulation diminution (GD-method) is applied. With this method the Readers themselves can determine their own limit distribution of all possible distributions which possess required qualitative features. The paper gives 3 such distributions determined by one of the authors that can directly be used in problems. It was also shown that the uniform distribution itself is the average, limit distribution of an infinite number of all possible distributions. According to the authors' knowledge the presented concept of the average, safe distribution is new in the scientific literature.