The sequencing problem in sequential investigation processes

Many decision problems in various fields of application can be characterized as diagnostic problems trying to assess the true state (of the world) of given cases. The investigation of assessment criteria improves the initial information according to observed signal outcomes, which are related to the possible states. Such sequential investigation processes can be analyzed within the framework of statistical decision theory, in which prior probability distributions of classes of cases are updated, allowing for a sorting of particular cases into ever smaller subclasses. However, receiving such information causes investigation costs. Besides the question about the set of relevant criteria, this defines two additional problems of statistical decision problems: the optimal stopping of investigations and the optimal sequence of investigating a given set of criteria. Unfortunately, no solution exists with which the optimal sequence can generally be determined. Therefore, the paper characterizes the associated problems and analyzes existing heuristics trying to approximate an optimal solution.