Inference with uncertain evidence

The subjectivist view of interpretation of Probability Theory considers probability to be the universal measure of uncertainty, and Bayes Theorem the principal rule for learning from evidence. In recent decades, alternative theories of uncertainty, including Possibility Theory and Evidence Theory, have been developed which seek to provide solutions for problems of evidential reasoning to which Bayes Theorem allegedly fails to apply. These problems can largely be characterized as cases of evidence uncertainty.; Evidence uncertainty occurs when the evidential meaning of observations is not well-defined. Possible causes include vagueness or ambiguity in descriptions of reality, lack of observational capabilities, and lack of definition of the representation of reality in which reasoning takes place.; This dissertation demonstrates that a probabilistic treatment of evidence uncertainty is possible. The solution method is based on a formalized notion of uncertain interpretation, which represents an observer's uncertainty about what can be concluded from an observation. Dependencies in the interpretations of multiple observations are treated by constructing joint interpretations, or alternatively by introducing assumptions on which interpretations are based as uncertain variables into the problem.; Inference takes place using a probabilistic rule of combination, which includes Bayes Theorem as a special case. This rule has the property that it performs simultaneous belief revision for the uncertain variables of interest and the assumptions on which interpretations are based. Observations are reinterpreted whenever new evidence is obtained.; It is concluded that the probabilistic treatment of uncertain evidence provides significant advantages over Bayes Theorem, particularly in terms of representing the evidential meaning of observations, and has behavioral characteristics that are intuitively appealing. It is further concluded that the rule of inference should be preferred over Evidence Theory and Possibility Theory, because of the solid conceptual background provided by Probability Theory.