Reasoning From Data in the Mathematical Theory of Evidence
This work addresses a foundational gap in MTE for researchers and practitioners in uncertainty reasoning, though it appears incremental as it builds on existing theory to resolve a known limitation.
The paper tackles the problem of integrating frequencies into the Mathematical Theory of Evidence (MTE), which has been criticized for lacking a connection to real-world data, by developing a frequentist model that enables data interpretation, random sampling, and comparison with MTE-based reasoning.
Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain open. One of the most important open questions seems to be the relationship between frequencies and the Mathematical Theory of Evidence. The theory is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to compare the performance of MTE-based models of real world processes against real world data. In this paper we develop a frequentist model of the MTE bringing to fall the above argument against MTE. We describe, how to interpret data in terms of MTE belief functions, how to reason from data about conditional belief functions, how to generate a random sample out of a MTE model, how to derive MTE model from data and how to compare results of reasoning in MTE model and reasoning from data. It is claimed in this paper that MTE is suitable to model some types of destructive processes