Probabilistic Knowledge Structures

Jean-Claude Falmagne () and Jean-Paul Doignon ()
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Jean-Claude Falmagne: University of California, Irvine, Department of Cognitive Sciences, Institute of Mathematical Behavioral Sciences
Jean-Paul Doignon: Université Libre de Bruxelles, Département de Mathématique

Chapter 11 in Learning Spaces, 2011, pp 187-214 from Springer

Abstract: Abstract The concept of a knowledge structure is a deterministic one. As such, it does not provide realistic predictions of subjects’ responses to the problems of a test. There are two ways in which probabilities must enter in a realistic model. For one, the knowledge states will certainly occur with different frequencies in the population of reference. It is thus reasonable to postulate the existence of a probability distribution on the collection of states. For another, a subject’s knowledge state does not necessarily specify the observed responses. A subject having mastered an item may be careless in responding, and make an error. Also, in some situations, a subject may be able to guess the correct response to a question not yet mastered. In general, it makes sense to introduce conditional probabilities of responses, given the states. A number of simple probabilistic models will be described in this chapter. They will be used to illustrate how probabilistic concepts can be introduced within knowledge space theory. These models will also provide a precise context for the discussion of some technical issues related to parameter estimation and statistical testing. The material in this chapter must be regarded as a preparation for the stochastic theories discussed in Chapters 12, 13 and 14.

Keywords: Response Pattern; State Probability; Knowledge Structure; Markov Chain Model; Knowledge State (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-01039-2_11

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