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The Value of Additional Knowledge in Measurement - a Bayesion Approach



Jürgen Beyerer


Measurement - Journal of the IMEKO, Elsevier, Vol. 25, No. 1, 1999.



The usefulness of additional knowledge in measurement is quantified in a relative way within the framework of Bayesian decision theory. The minimal risks of two states of information I and II are compared, where I is the initial state and II comprises I as well as the additional knowledge which is to be assessed. To obtain meaningful results, appropriate loss actions are to be chosen for different scales of measurement. The alternative of assessing the worth of additional knowledge with methods of classical statistics by comparing lower bounds (e.g. Cramér Rao or Barankin) on the estimation errors for I and II is also mentioned, and pertaining difficulties are discussed. Two examples show that the Bayesian approach is not really a means for assessing the relevance of additional knowledge quantitatively, but it also gives some insight into the innerplay of observed data and additional knowledge.