Bayesian Decision Analysis

Abstract

Statistics and probability theory forms the foundation for the quantification of knowledge and the utilization of this knowledge for the purpose of supporting decision making. In the foregoing chapters all the prerequisites have been established for the modeling and assessment of the probabilities which are required in order to assess the risks. In the present and final chapter of this book the basic decision analysis framework and the fundamental techniques are presented which facilitates that risk may be utilized for assessing and ranking decision alternatives and thereby enabling optimal decisions and supporting sustainable societal development.

In Lecture 13, first the concept of decision/event trees is introduced and on this basis, with the help of an example considering an engineering decision problem on how to establish a fresh water supply system, three fundamental Bayesian decision analyses formulations are presented and explained. The first formulation is the prior decision analysis which is utilized for the ranking of decision alternatives on the basis of the available (prior) knowledge. Using the posterior decision analysis it is shown how the prior knowledge may be updated on the basis of new information to enhance the optimal choice of decisions. Finally, it is shown how the powerful pre-posterior decision analysis may be utilized to assess the value of information, which has not yet been achieved, and thereby support decisions on how to improve the state of knowledge optimally in the context of a given decision problem.