Observation Value Analysis – Integral Part of Bayesian Diagnostics

The decision making process, in general, is understood as a process of selecting one of the available solutions to the problem. One of possible approaches supporting the process is Bayesian statistical decision theory providing a mathematical model to make decisions of a technical nature in conditions of uncertainty. Regarding above, a detailed subject of the research is to analyze the value of the observation, which is a part of preposterior analysis. For the presented network, the main objective was to determine, conducting of which of three tests is the most valuable from the perspective of determining possible need or possibility to omission expensive technical expertise. The basis of verification, which test is the most valuable, is therefore the comparison of expected value of sample information (EVSI) for each of the three tests.The main advantage of preposterior analysis is answering the question which of the considered experiments is potentially the best source of information and what cost needs to be incurred on its execution (price of new information). If the cost of such an examination is relatively small compared to the value of information on the state of nature, this implies a direct recommendation to conduct the experiment.In conclusion, the construction of the decision-making model being a reflection of the state of nature allows to determine the ranking of decisions, including those regarding selection of the optimal test. It is noteworthy, that test result itself can contribute to an increase in the expected value of the decision involved, but on the other hand, the reduction of uncertainty may be considerably outweighed to the necessity to incur expenses for this examination.