Empirical studies in the application of Dempster-Shafer belief functions: An alternative calculus for representing degrees of belief.

摘要

Representation systems provide a language with which to communicate a scaling of the strength of our beliefs. Having a language provides a guide and justification for actions based on our beliefs, and helps us to understand how evidence affects the formulation and evolution of beliefs. While the best-known representational system for communicating degrees of belief is probability theory, this thesis examines an alternative system: Dempster-Shafer belief functions.;First, the thesis provides an introduction to representational systems and motivates the empirical investigation of belief functions. The potential usefulness of belief functions as an alternative representational system is highlighted by contrasting belief functions with probability functions. These contrasts include belief functions' focus on the representation of justification, accommodation of non-complementary belief revision, and context-independent representation of ignorance. Finally, a criminal legal setting, emphasizing justification, is advanced as an appropriate domain for the empirical investigation of belief functions.;Next, the thesis defines the aspects of Dempster-Shafer theory relevant to its experiments. These definitions include those aspects required to represent individual evidence, as well as the aggregation of evidence through Dempster's rule of combination. Additionally, four other combination rules are introduced and contrasted with Dempster's rule.;Next, the thesis operationalizes meaningfulness in the application of belief functions. Three measures, structural validity, reliability, and numerical validity are defined for evaluating the meaningfulness of belief function assessments. Then, two experiments are presented in which subjects' assessments are analyzed with respect to the measures of meaningfulness. The results show that subjects can use belief functions to meaningfully communicate their beliefs. Specifically, subjects' assessed beliefs were structurally consistent with the expectations of Dempster-Shafer theory, reliable over multiple assessment periods, and capable of distinguishing and ordering different strengths of evidence. Besides evaluating meaningfulness in individual evidence, subjects' aggregations of evidence were examined and compared with Dempster's rule and the four alternative combination rules. Dempster's rule and a conflict-to-theta rule were reasonably descriptive of subjects' aggregations.;Finally, the implications of the finding that people can meaningfully communicate through belief functions is discussed and additional research is suggested.