Evaluating Credal Set Theory as a Belief Framework in High-Level Information Fusion for Automated Decision-Making

The goal of high-level information fusion is to provide effective decision-support regarding situations, e.g., relations between events. One of the main ways that has been proposed in order to achieve this is to reduce uncertainty regarding the situation by utilizing multiple sources of information. There exist two types of uncertainty: aleatory and epistemic. Aleatory uncertainty, also known as uncertainty due to chance, cannot be reduced regardless of the amount of information. Epistemic uncertainty, on the other hand, also known as uncertainty due to lack of information, can be reduced if more information becomes available. Since the goal of high-level information fusion states that we want to reduce uncertainty by utilizing information, we conclude that the type of uncertainty referred to is epistemic in nature. Uncertainty in high-level information fusion is most often expressed via a belief framework. The most common such framework in high-level information fusion is precise Bayesian theory. In this thesis proposal we argue that precise Bayesian theory cannot adequately represent epistemic uncertainty and that there exists another belief framework referred to as credal set theory that possesses this ability. This can actually be demonstrated by such simple as tossing a coin. In precise Bayesian theory, assuming no prior information about the coin, the same probability of “Head” can be adopted as the belief before any information is available, as a prior, as well as later when a large amount of information is available, as a posterior. By utilizing credal set theory, where a credal set is defined as a closed convex set of probability measures, this case amounts to representing the prior of “Head” as a probability interval, and a posterior with a smaller interval. The idea is that when a large amount of information is available, the interval converges into a point, i.e., the length of the interval, or degree of imprecision, reflects the degree of epistemic uncertainty. In precise Bayesian theory, a common automated decision-making strategy is to decide for the action that maximizes the expected utility with respect to a utility function and a probability measure. Since the probability measure cannot adequately reflect the amount of information of which it is based on, this is an approach that does not take epistemic uncertainty into consideration, i.e., it is possible to decide for an action based on a high degree of epistemic uncertainty, and not even be aware of it. By utilizing credal set theory, epistemic uncertainty is reflected by imprecision in both probabilities and expected utilities. The main problem addressed in this thesis proposal is to decide if better automated decisions can be made by utilizing credal set theory as a belief framework in high-level information fusion, in comparison to precise Bayesian theory. The research question addressed is whether it is possible to characterize, in terms of degree of epistemic uncertainty, when and why one framework is better suited than the other for this purpose.