Surmise relations between tests—mathematical considerations

Surmise Relations Between Tests - Mathematical Considerations

In 1985, Doignon and Falmagne introduced surmise relations for representing prerequisite relationships between items within a body of information for the assessment of knowledge. Often it is useful to partition such a body of information into sub-collections. As we are primarily interested in psychological applications, we refer to these sub-collections as tests. We extend the concept of surmis...

Ordering Inductive Reasoning Tests for Adaptive Knowledge Assessments An Application of Surmise Relations between Tests

Test Surmise Relations, Test Knowledge Structures, and Their Characterizations

This paper investigates natural, left-, right-, and total-covering test surmise relations on a set of tests partitioning the domain of a knowledge structure. The properties of reflexivity, transitivity, and antisymmetry are examined. In particular, it is shown that the property of antisymmetry is satisfied for the left-, right-, and total-covering test surmise relations when the underlying know...

Relations between Renyi Distance and Fisher Information

In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher information of their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi dis...

Reasoning about the relations between relations.

Relations can hold between relations, as in assertions such as: Cordelia loves Lear more than Goneril does. Naïve reasoners can make inferences that depend on these higher order relations, which are vital for science and mathematics, but no existing theory explains such inferences. The present paper presents a theory based on mental models of the situations under description, and it reports fou...